Theorem csbeq2dv 2015

Description: Formula-building deduction rule for class substitution.

Hypothesis

Ref	Expression
csbeq2dv.1	|- (ph -> B = C)

Assertion

Ref	Expression
csbeq2dv	|- ((ph /\ A e. D) -> [_A / x]_B = [_A / x]_C)

Distinct variable group:   ph,x

Proof of Theorem csbeq2dv

Step	Hyp	Ref	Expression
1		ax-17 969	. 2 |- (ph -> A.xph)
2		csbeq2dv.1	. 2 |- (ph -> B = C)
3	1, 2	csbeq2d 2014	1 |- ((ph /\ A e. D) -> [_A / x]_B = [_A / x]_C)

Syntax hints:   -> wi 3   /\ wa 223   = wceq 954   e. wcel 956  [_csb 1997

This theorem is referenced by:  csbnestg 2032  csbfsumlem 6972

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-9 963  ax-10 964  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-3an 776  df-ex 979  df-sb 1170  df-clab 1462  df-cleq 1467  df-clel 1470  df-v 1808  df-sbc 1938  df-csb 1998

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