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Theorem coeq2i 4957
Description: Equality inference for composition of two classes. (Contributed by NM, 16-Nov-2000.)
Hypothesis
Ref Expression
coeq1i.1  |-  A  =  B
Assertion
Ref Expression
coeq2i  |-  ( C  o.  A )  =  ( C  o.  B
)

Proof of Theorem coeq2i
StepHypRef Expression
1 coeq1i.1 . 2  |-  A  =  B
2 coeq2 4955 . 2  |-  ( A  =  B  ->  ( C  o.  A )  =  ( C  o.  B ) )
31, 2ax-mp 5 1  |-  ( C  o.  A )  =  ( C  o.  B
)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1437    o. ccom 4800
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2558  df-in 3386  df-ss 3393  df-br 4367  df-opab 4426  df-co 4805
This theorem is referenced by:  coeq12i  4960  cocnvcnv2  5309  co01  5312  fcoi1  5717  dftpos2  6945  tposco  6959  canthp1  9030  cats1co  12898  isoval  15613  mvdco  17029  evlsval  18685  evl1fval1lem  18861  evl1var  18867  pf1ind  18886  imasdsf1olem  21330  hoico1  27351  hoid1i  27384  pjclem1  27790  pjclem3  27792  pjci  27795  dfpo2  30346  poimirlem9  31856  cdlemk45  34426  cononrel1  36113  trclubgNEW  36138  trclrelexplem  36216  relexpaddss  36223  cotrcltrcl  36230  cortrcltrcl  36245  corclrtrcl  36246  cotrclrcl  36247  cortrclrcl  36248  cotrclrtrcl  36249  cortrclrtrcl  36250  meadjiun  38155
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