Theorem opreqan12rd 3980

Description: Equality deduction for operation value.

Hypotheses

Ref	Expression
opreq1d.1	|- (ph -> A = B)
opreqan12i.2	|- (ps -> C = D)

Assertion

Ref	Expression
opreqan12rd	|- ((ps /\ ph) -> (AFC) = (BFD))

Proof of Theorem opreqan12rd

Step	Hyp	Ref	Expression
1		opreq1d.1	. . 3 |- (ph -> A = B)
2		opreqan12i.2	. . 3 |- (ps -> C = D)
3	1, 2	opreqan12d 3979	. 2 |- ((ph /\ ps) -> (AFC) = (BFD))
4	3	ancoms 436	1 |- ((ps /\ ph) -> (AFC) = (BFD))

Syntax hints:   -> wi 3   /\ wa 223   = wceq 956  (class class class)co 3963

This theorem is referenced by:  mulgt0sr 5214  mulcnsr 5254  mulresr 5257  recdivt 5790  seq1res 6327  seqzfveq 6554  fsumcom 7028  nonbool 9596  0cnop 9903  0cnfn 9904  idcnop 9905  idfisf 10760

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-11 967  ax-12 968  ax-13 969  ax-14 970  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459  ax-sep 2703  ax-pow 2742  ax-pr 2779

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-eu 1382  df-mo 1383  df-clab 1464  df-cleq 1469  df-clel 1472  df-ne 1587  df-v 1812  df-dif 2049  df-un 2050  df-in 2051  df-ss 2053  df-nul 2281  df-pw 2402  df-sn 2412  df-pr 2413  df-op 2416  df-uni 2504  df-br 2620  df-opab 2667  df-xp 3184  df-cnv 3186  df-dm 3188  df-rn 3189  df-res 3190  df-ima 3191  df-fv 3198  df-opr 3965

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