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Theorem coeq12i 5441
 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 (𝐴𝐶) = (𝐵𝐷)

Proof of Theorem coeq12i
StepHypRef Expression
1 coeq12i.1 . . 3 𝐴 = 𝐵
21coeq1i 5437 . 2 (𝐴𝐶) = (𝐵𝐶)
3 coeq12i.2 . . 3 𝐶 = 𝐷
43coeq2i 5438 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2782 1 (𝐴𝐶) = (𝐵𝐷)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1632   ∘ ccom 5270 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-in 3722  df-ss 3729  df-br 4805  df-opab 4865  df-co 5275 This theorem is referenced by:  madetsumid  20469  mdetleib2  20596  imsval  27849  pjcmul1i  29369  cotrcltrcl  38519  brtrclfv2  38521  clsneif1o  38904
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