Theorem csbeq2i 3164

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 3163	. 2 |- ( T. -> [_ A / x ]_ B = [_ A / x ]_ C )
4	3	mptru 1407	1 |- [_ A / x ]_ B = [_ A / x ]_ C

Syntax hints:   = wceq 1398   T. wtru 1399   [_csb 3137

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-sbc 3042  df-csb 3138

This theorem is referenced by:  csbvarg  3165  csbnest1g  3193  csbsng  3749  csbunig  3921  csbxpg  4830  csbcnvg  4938  csbdmg  4949  csbresg  5040  csbrng  5223  csbfv12g  5709  csbnegg  8470  iseqf1olemjpcl  10869  iseqf1olemqpcl  10870  iseqf1olemfvp  10871  seq3f1olemqsum  10874  csbwrdg  11250