Theorem csbeq2i 2933

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 2932	. 2 |- ( T. -> [_ A / x ]_ B = [_ A / x ]_ C )
4	3	trud 1294	1 |- [_ A / x ]_ B = [_ A / x ]_ C

Syntax hints:   = wceq 1285   T. wtru 1286   [_csb 2909

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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064

This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-sbc 2817  df-csb 2910

This theorem is referenced by:  csbvarg  2934  csbnest1g  2958  csbsng  3461  csbunig  3617  csbxpg  4447  csbcnvg  4547  csbdmg  4557  csbresg  4643  csbrng  4812  csbfv12g  5241  csbnegg  7373