Theorem coeq12i 4761

Description: Equality inference for composition of two classes. (Contributed by FL, 7-Jun-2012.)

Hypotheses

Ref	Expression
coeq12i.1	|- A = B
coeq12i.2	|- C = D

Assertion

Ref	Expression
coeq12i	|- ( A o. C ) = ( B o. D )

Proof of Theorem coeq12i

Step	Hyp	Ref	Expression
1		coeq12i.1	. . 3 |- A = B
2	1	coeq1i 4757	. 2 |- ( A o. C ) = ( B o. C )
3		coeq12i.2	. . 3 |- C = D
4	3	coeq2i 4758	. 2 |- ( B o. C ) = ( B o. D )
5	2, 4	eqtri 2185	1 |- ( A o. C ) = ( B o. D )

Syntax hints:   = wceq 1342   o. ccom 4602

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146

This theorem depends on definitions:  df-bi 116  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-nfc 2295  df-in 3117  df-ss 3124  df-br 3977  df-opab 4038  df-co 4607

This theorem is referenced by: (None)