Theorem csbeq2i 2932

Description: Formula-building inference rule 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 2931	. 2 |- ( T. -> [_ A / x ]_ B = [_ A / x ]_ C )
4	3	trud 1293	1 |- [_ A / x ]_ B = [_ A / x ]_ C

Syntax hints:   = wceq 1284   T. wtru 1285   [_csb 2908

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-11 1437  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-sbc 2816  df-csb 2909

This theorem is referenced by:  csbvarg  2933  csbnest1g  2957  csbsng  3453  csbunig  3609  csbxpg  4439  csbcnvg  4537  csbdmg  4547  csbresg  4633  csbrng  4802  csbfv12g  5230  csbnegg  7306