Theorem coeq12i 4774

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 4770	. 2 |- ( A o. C ) = ( B o. C )
3		coeq12i.2	. . 3 |- C = D
4	3	coeq2i 4771	. 2 |- ( B o. C ) = ( B o. D )
5	2, 4	eqtri 2191	1 |- ( A o. C ) = ( B o. D )

Syntax hints:   = wceq 1348   o. ccom 4615

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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-in 3127  df-ss 3134  df-br 3990  df-opab 4051  df-co 4620

This theorem is referenced by: (None)