Theorem coeq12i 4880

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 ∘ C) = (B ∘ D)

Proof of Theorem coeq12i

Step	Hyp	Ref	Expression
1		coeq12i.1	. . 3 ⊢ A = B
2	1	coeq1i 4876	. 2 ⊢ (A ∘ C) = (B ∘ C)
3		coeq12i.2	. . 3 ⊢ C = D
4	3	coeq2i 4877	. 2 ⊢ (B ∘ C) = (B ∘ D)
5	2, 4	eqtri 2373	1 ⊢ (A ∘ C) = (B ∘ D)

Syntax hints:   = wceq 1642   ∘ ccom 4721

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-opab 4623  df-br 4640  df-co 4726

This theorem is referenced by:  cnvpprod  5841