Theorem csbeq2i 3168

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 3167	. 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 3141

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 2216

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-sbc 3046  df-csb 3142

This theorem is referenced by:  csbvarg  3169  csbnest1g  3197  csbsng  3756  csbunig  3928  csbxpg  4837  csbcnvg  4945  csbdmg  4956  csbresg  5047  csbrng  5230  csbfv12g  5716  csbnegg  8489  iseqf1olemjpcl  10898  iseqf1olemqpcl  10899  iseqf1olemfvp  10900  seq3f1olemqsum  10903  csbwrdg  11283