Theorem coeq2i 4126

Description: Equality inference for composition of two classes.

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 4124	. 2 |- (A = B -> (C o. A) = (C o. B))
3	1, 2	ax-mp 7	1 |- (C o. A) = (C o. B)

Syntax hints:   = wceq 1298   o. ccom 3990

This theorem is referenced by:  cocnvcnv2 4409  co01 4412  fcoi1 4584  fparlem3 5083  fparlem4 5084  mapenlem2 5584  seq1val 7725  hoico1 11319  hoid1i 11352  pjclem1 11768  pjclem3 11770  pjci 11773  pjcmmul1i 11774  eucalgcvga 13754  mulgcdlem5 13760

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-10 1308  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-16 1580  ax-11o 1588  ax-ext 1865

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-sb 1536  df-clab 1872  df-cleq 1877  df-clel 1880  df-br 3339  df-opab 3396  df-co 4003

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