Theorem csbeq1d 2939

Description: Equality deduction for proper substitution into a class. (Contributed by NM, 3-Dec-2005.)

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 2936	. 2 |- ( A = B -> [_ A / x ]_ C = [_ B / x ]_ C )
3	1, 2	syl 14	1 |- ( ph -> [_ A / x ]_ C = [_ B / x ]_ C )

Syntax hints:   -> wi 4   = wceq 1289   [_csb 2933

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-sbc 2841  df-csb 2934

This theorem is referenced by:  csbidmg  2984  csbco3g  2986  fmptcof  5459  mpt2mptsx  5959  dmmpt2ssx  5961  fmpt2x  5962  fmpt2co  5973  xpf1o  6550  isummolem3  10757  isummolem2a  10758  isummo  10760  zisum  10761  fisum  10765  sumsnf  10790  fsumcnv  10818  fisumcom2  10819  fsumshftm  10826  fisum0diag2  10828