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Theorem coeq12i 5522
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 5518 . 2 (𝐴𝐶) = (𝐵𝐶)
3 coeq12i.2 . . 3 𝐶 = 𝐷
43coeq2i 5519 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2849 1 (𝐴𝐶) = (𝐵𝐷)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1656  ccom 5350
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-13 2389  ax-ext 2803
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-in 3805  df-ss 3812  df-br 4876  df-opab 4938  df-co 5355
This theorem is referenced by:  madetsumid  20642  mdetleib2  20769  imsval  28091  pjcmul1i  29611  cotrcltrcl  38853  brtrclfv2  38855  clsneif1o  39237
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