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Theorem coeq12i 5028
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  o.  C )  =  ( B  o.  D
)

Proof of Theorem coeq12i
StepHypRef Expression
1 coeq12i.1 . . 3  |-  A  =  B
21coeq1i 5024 . 2  |-  ( A  o.  C )  =  ( B  o.  C
)
3 coeq12i.2 . . 3  |-  C  =  D
43coeq2i 5025 . 2  |-  ( B  o.  C )  =  ( B  o.  D
)
52, 4eqtri 2455 1  |-  ( A  o.  C )  =  ( B  o.  D
)
Colors of variables: wff set class
Syntax hints:    = wceq 1652    o. ccom 4874
This theorem is referenced by:  imsval  22169  pjcmul1i  23696
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-in 3319  df-ss 3326  df-br 4205  df-opab 4259  df-co 4879
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