Theorem csbeq2i 3034

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 3033	. 2 |- ( T. -> [_ A / x ]_ B = [_ A / x ]_ C )
4	3	mptru 1341	1 |- [_ A / x ]_ B = [_ A / x ]_ C

Syntax hints:   = wceq 1332   T. wtru 1333   [_csb 3007

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-sbc 2914  df-csb 3008

This theorem is referenced by:  csbvarg  3035  csbnest1g  3060  csbsng  3592  csbunig  3752  csbxpg  4628  csbcnvg  4731  csbdmg  4741  csbresg  4830  csbrng  5008  csbfv12g  5465  csbnegg  7984  iseqf1olemjpcl  10299  iseqf1olemqpcl  10300  iseqf1olemfvp  10301  seq3f1olemqsum  10304