Theorem csbeq2i 3155

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 3154	. 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 3128

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 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-sbc 3033  df-csb 3129

This theorem is referenced by:  csbvarg  3156  csbnest1g  3184  csbsng  3734  csbunig  3906  csbxpg  4813  csbcnvg  4920  csbdmg  4931  csbresg  5022  csbrng  5205  csbfv12g  5688  csbnegg  8420  iseqf1olemjpcl  10814  iseqf1olemqpcl  10815  iseqf1olemfvp  10816  seq3f1olemqsum  10819  csbwrdg  11190