Theorem csbeq1d 2004

Description: Equality deduction for proper substitution into a class.

Hypothesis

Ref	Expression
csbeq1d.1	|- (ph -> A = B)

Assertion

Ref	Expression
csbeq1d	|- (ph -> [_A / x]_C = [_B / x]_C)

Proof of Theorem csbeq1d

Step	Hyp	Ref	Expression
1		csbeq1d.1	. 2 |- (ph -> A = B)
2		csbeq1 2003	. 2 |- (A = B -> [_A / x]_C = [_B / x]_C)
3	1, 2	syl 10	1 |- (ph -> [_A / x]_C = [_B / x]_C)

Syntax hints:   -> wi 3   = wceq 956  [_csb 2001

This theorem is referenced by:  csbnestglem 2035  csbnestg 2036  csbnest1g 2037  csbidmg 2039  csbco3g 2040  fsump1slem 7012  fsum3 7024  fsum4 7025  fsumrev 7029  fsumshft 7031  fsum0diaglem2 7257  fsum0diag 7258  fsum0diag2 7259  fsum0diag4 7261

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-sbc 1942  df-csb 2002

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