Theorem csbeq2i 3152

Description: Formula-building inference for class substitution. (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.)

Hypothesis

Ref	Expression
csbeq2i.1	|- B = C

Assertion

Ref	Expression
csbeq2i	|- [_ A / x ]_ B = [_ A / x ]_ C

Proof of Theorem csbeq2i

Step	Hyp	Ref	Expression
1		csbeq2i.1	. . . 4 |- B = C
2	1	a1i 9	. . 3 |- ( T. -> B = C )
3	2	csbeq2dv 3151	. 2 |- ( T. -> [_ A / x ]_ B = [_ A / x ]_ C )
4	3	mptru 1404	1 |- [_ A / x ]_ B = [_ A / x ]_ C

Syntax hints:   = wceq 1395   T. wtru 1396   [_csb 3125

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-sbc 3030  df-csb 3126

This theorem is referenced by:  csbvarg  3153  csbnest1g  3181  csbsng  3728  csbunig  3897  csbxpg  4803  csbcnvg  4910  csbdmg  4921  csbresg  5012  csbrng  5194  csbfv12g  5673  csbnegg  8365  iseqf1olemjpcl  10758  iseqf1olemqpcl  10759  iseqf1olemfvp  10760  seq3f1olemqsum  10763  csbwrdg  11130