Theorem coeq2d 3283

Description: Equality deduction for composition of two classes.

Hypothesis

Ref	Expression
coeq1d.1	|- (ph -> A = B)

Assertion

Ref	Expression
coeq2d	|- (ph -> (C o. A) = (C o. B))

Proof of Theorem coeq2d

Step	Hyp	Ref	Expression
1		coeq1d.1	. 2 |- (ph -> A = B)
2		coeq2 3279	. 2 |- (A = B -> (C o. A) = (C o. B))
3	1, 2	syl 10	1 |- (ph -> (C o. A) = (C o. B))

Syntax hints:   -> wi 3   = wceq 955   o. ccom 3171

This theorem is referenced by:  f1ococnv1 3706  mapenlem1 4482  mapenlem2 4483  imsval 8302  hoddit 9906  kbass2t 10041  kbass5t 10044

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-12 967  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 980  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-br 2617  df-opab 2664  df-co 3184

Copyright terms: Public domain