Theorem csbeq2dv 2019

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-17 971	. 2 |- (ph -> A.xph)
2		csbeq2dv.1	. 2 |- (ph -> B = C)
3	1, 2	csbeq2d 2018	1 |- ((ph /\ A e. D) -> [_A / x]_B = [_A / x]_C)

Syntax hints:   -> wi 3   /\ wa 223   = wceq 956   e. wcel 958  [_csb 2001

This theorem is referenced by:  csbnestg 2036  csbfsumlem 7026

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-9 965  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-or 224  df-an 225  df-3an 777  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1812  df-sbc 1942  df-csb 2002

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