Theorem coeq2i 4707

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

Step	Hyp	Ref	Expression
1		coeq1i.1	. 2 |- A = B
2		coeq2 4705	. 2 |- ( A = B -> ( C o. A ) = ( C o. B ) )
3	1, 2	ax-mp 5	1 |- ( C o. A ) = ( C o. B )

Syntax hints:   = wceq 1332   o. ccom 4551

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-in 3082  df-ss 3089  df-br 3938  df-opab 3998  df-co 4556

This theorem is referenced by:  coeq12i  4710  cocnvcnv2  5058  co01  5061  cocnvres  5071  fcoi1  5311  dftpos2  6166  tposco  6180