Theorem csbeq2i 3836

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 11	. . 3 |- ( T. -> B = C )
3	2	csbeq2dv 3835	. 2 |- ( T. -> [_ A / x ]_ B = [_ A / x ]_ C )
4	3	trud 1388	1 |- [_ A / x ]_ B = [_ A / x ]_ C

Syntax hints:   = wceq 1379   T. wtru 1380   [_csb 3435

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-sbc 3332  df-csb 3436

This theorem is referenced by:  csbnest1g  3845  csbvarg  3848  csbsng  4086  csbprg  4087  csbuni  4273  csbunigOLD  4274  csbmpt12  4781  csbxp  5079  csbxpgOLD  5080  csbcnv  5184  csbcnvgALT  5185  csbdm  5195  csbres  5274  csbresgOLD  5275  csbrn  5466  csbrngOLD  5467  csbfv12  5899  csbfv12gOLD  5900  fvmpt2curryd  6997  csbnegg  9813  csbwrdg  12530  matgsum  18703  disjxpin  27117  csbfv12gALTOLD  32701  csbima12gALTOLD  32702  bj-csbsn  33552  cdleme31so  35175  cdleme31sn  35176  cdleme31sn1  35177  cdleme31se  35178  cdleme31se2  35179  cdleme31sc  35180  cdleme31sde  35181  cdleme31sn2  35185  cdlemkid3N  35729  cdlemkid4  35730