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Theorem coeq12i 4847
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 4843 . 2  |-  ( A  o.  C )  =  ( B  o.  C
)
3 coeq12i.2 . . 3  |-  C  =  D
43coeq2i 4844 . 2  |-  ( B  o.  C )  =  ( B  o.  D
)
52, 4eqtri 2303 1  |-  ( A  o.  C )  =  ( B  o.  D
)
Colors of variables: wff set class
Syntax hints:    = wceq 1623    o. ccom 4693
This theorem is referenced by:  imsval  21254  pjcmul1i  22781  cmp2morpgrp  25963
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-in 3159  df-ss 3166  df-br 4024  df-opab 4078  df-co 4698
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