Theorem coeq12i 4697

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 4693	. 2 |- ( A o. C ) = ( B o. C )
3		coeq12i.2	. . 3 |- C = D
4	3	coeq2i 4694	. 2 |- ( B o. C ) = ( B o. D )
5	2, 4	eqtri 2158	1 |- ( A o. C ) = ( B o. D )

Syntax hints:   = wceq 1331   o. ccom 4538

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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-in 3072  df-ss 3079  df-br 3925  df-opab 3985  df-co 4543

This theorem is referenced by: (None)