Theorem sseq12i 2090

Description: An equality inference for the subclass relationship. (The proof was shortened by Eric Schmidt, 26-Jan-2007.)

Hypotheses

Ref	Expression
sseq1i.1	|- A = B
sseq12i.2	|- C = D

Assertion

Ref	Expression
sseq12i	|- (A (_ C <-> B (_ D)

Proof of Theorem sseq12i

Step	Hyp	Ref	Expression
1		sseq1i.1	. 2 |- A = B
2		sseq12i.2	. 2 |- C = D
3		sseq12 2087	. 2 |- ((A = B /\ C = D) -> (A (_ C <-> B (_ D))
4	1, 2, 3	mp2an 699	1 |- (A (_ C <-> B (_ D)

Syntax hints:   <-> wb 146   = wceq 958   (_ wss 2050

This theorem is referenced by:  3sstr3 2102  3sstr4 2103  3sstr3g 2104  3sstr4g 2105  ss2rab 2126  rabss2 2132  ssopab2 2828  shlub 9341  pjord 10096  mdsldmd1 10253

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-in 2054  df-ss 2056

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