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Theorem coeq12i 4976
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 4972 . 2  |-  ( A  o.  C )  =  ( B  o.  C
)
3 coeq12i.2 . . 3  |-  C  =  D
43coeq2i 4973 . 2  |-  ( B  o.  C )  =  ( B  o.  D
)
52, 4eqtri 2407 1  |-  ( A  o.  C )  =  ( B  o.  D
)
Colors of variables: wff set class
Syntax hints:    = wceq 1649    o. ccom 4822
This theorem is referenced by:  imsval  22025  pjcmul1i  23552
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-in 3270  df-ss 3277  df-br 4154  df-opab 4208  df-co 4827
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