Theorem coeq12i 4825

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 4821	. 2 |- ( A o. C ) = ( B o. C )
3		coeq12i.2	. . 3 |- C = D
4	3	coeq2i 4822	. 2 |- ( B o. C ) = ( B o. D )
5	2, 4	eqtri 2214	1 |- ( A o. C ) = ( B o. D )

Syntax hints:   = wceq 1364   o. ccom 4663

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-in 3159  df-ss 3166  df-br 4030  df-opab 4091  df-co 4668

This theorem is referenced by: (None)