Theorem coeq1i 4800

Description: Equality inference for composition of two classes. (Contributed by NM, 16-Nov-2000.)

Hypothesis

Ref	Expression
coeq1i.1	|- A = B

Assertion

Ref	Expression
coeq1i	|- ( A o. C ) = ( B o. C )

Proof of Theorem coeq1i

Step	Hyp	Ref	Expression
1		coeq1i.1	. 2 |- A = B
2		coeq1 4798	. 2 |- ( A = B -> ( A o. C ) = ( B o. C ) )
3	1, 2	ax-mp 5	1 |- ( A o. C ) = ( B o. C )

Syntax hints:   = wceq 1363   o. ccom 4644

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2170

This theorem depends on definitions:  df-bi 117  df-nf 1471  df-sb 1773  df-clab 2175  df-cleq 2181  df-clel 2184  df-nfc 2320  df-in 3149  df-ss 3156  df-br 4018  df-opab 4079  df-co 4649

This theorem is referenced by:  coeq12i  4804  cocnvcnv1  5153  upxp  14155  uptx  14157