Theorem coeq2i 3284

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 3282	. 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 956   o. ccom 3174

This theorem is referenced by:  cocnvcnv2 3506  co01 3509  mapenlem2 4490  seq1val 6312  hoico1t 9682  hoid1 9715  pjclem1 10123  pjclem3 10125  pjc 10128  pjcmmul1 10129

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-br 2620  df-opab 2667  df-co 3187

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