Theorem coeq1i 3278

Description: Equality inference for composition of two classes.

Hypothesis

Ref	Expression
coeq1i.1	|- A = B

Assertion

Ref	Expression
coeq1i	|- (A o. C) = (B o. C)

Proof of Theorem coeq1i

Step	Hyp	Ref	Expression
1		coeq1i.1	. 2 |- A = B
2		coeq1 3276	. 2 |- (A = B -> (A o. C) = (B o. C))
3	1, 2	ax-mp 7	1 |- (A o. C) = (B o. C)

Syntax hints:   = wceq 954   o. ccom 3169

This theorem is referenced by:  cocnvcnv1 3497  cores2 3499  mapenlem2 4476  seq1suclem 6261  hoico2t 9623  hoid1r 9656  adjbdlnb 9955  nmopcoadj2 9973  pjclem3 10063  pjcmmul1 10067

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 979  df-sb 1170  df-clab 1462  df-cleq 1467  df-clel 1470  df-br 2615  df-opab 2662  df-co 3182

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