Theorem coeq12i 4785

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 4781	. 2 |- ( A o. C ) = ( B o. C )
3		coeq12i.2	. . 3 |- C = D
4	3	coeq2i 4782	. 2 |- ( B o. C ) = ( B o. D )
5	2, 4	eqtri 2198	1 |- ( A o. C ) = ( B o. D )

Syntax hints:   = wceq 1353   o. ccom 4626

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-in 3135  df-ss 3142  df-br 4001  df-opab 4062  df-co 4631

This theorem is referenced by: (None)