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Theorem coeq12i 5728
 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 5724 . 2 (𝐴𝐶) = (𝐵𝐶)
3 coeq12i.2 . . 3 𝐶 = 𝐷
43coeq2i 5725 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2844 1 (𝐴𝐶) = (𝐵𝐷)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1533   ∘ ccom 5553 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2157  ax-12 2173  ax-ext 2793 This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1536  df-ex 1777  df-nf 1781  df-sb 2066  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-in 3942  df-ss 3951  df-br 5059  df-opab 5121  df-co 5558 This theorem is referenced by:  madetsumid  21064  mdetleib2  21191  imsval  28456  pjcmul1i  29972  coprprop  30429  cotrcltrcl  40063  brtrclfv2  40065  clsneif1o  40447
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