Theorem csbeq2i 3111

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 3110	. 2 |- ( T. -> [_ A / x ]_ B = [_ A / x ]_ C )
4	3	mptru 1373	1 |- [_ A / x ]_ B = [_ A / x ]_ C

Syntax hints:   = wceq 1364   T. wtru 1365   [_csb 3084

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-11 1520  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-sbc 2990  df-csb 3085

This theorem is referenced by:  csbvarg  3112  csbnest1g  3140  csbsng  3683  csbunig  3847  csbxpg  4744  csbcnvg  4850  csbdmg  4860  csbresg  4949  csbrng  5131  csbfv12g  5596  csbnegg  8224  iseqf1olemjpcl  10600  iseqf1olemqpcl  10601  iseqf1olemfvp  10602  seq3f1olemqsum  10605  csbwrdg  10964