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Theorem coeq12i 5195
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 5191 . 2 (𝐴𝐶) = (𝐵𝐶)
3 coeq12i.2 . . 3 𝐶 = 𝐷
43coeq2i 5192 . 2 (𝐵𝐶) = (𝐵𝐷)
52, 4eqtri 2631 1 (𝐴𝐶) = (𝐵𝐷)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1474  ccom 5032
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-in 3546  df-ss 3553  df-br 4578  df-opab 4638  df-co 5037
This theorem is referenced by:  madetsumid  20028  mdetleib2  20155  imsval  26721  pjcmul1i  28250  cotrcltrcl  36832  brtrclfv2  36834  clsneif1o  37218
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