Theorem csbeq2dv 3150

Description: Formula-building deduction for class substitution. (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.)

Hypothesis

Ref	Expression
csbeq2dv.1	|- ( ph -> B = C )

Assertion

Ref	Expression
csbeq2dv	|- ( ph -> [_ A / x ]_ B = [_ A / x ]_ C )

Distinct variable group:   ph, x

Allowed substitution hints:   A( x)   B( x)   C( x)

Proof of Theorem csbeq2dv

Step	Hyp	Ref	Expression
1		nfv 1574	. 2 |- F/ x ph
2		csbeq2dv.1	. 2 |- ( ph -> B = C )
3	1, 2	csbeq2d 3149	1 |- ( ph -> [_ A / x ]_ B = [_ A / x ]_ C )

Syntax hints:   -> wi 4   = wceq 1395   [_csb 3124

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 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-sbc 3029  df-csb 3125

This theorem is referenced by:  csbeq2i  3151  mpomptsx  6333  dmmpossx  6335  fmpox  6336  fmpoco  6352  fisumcom2  11935  fprodcom2fi  12123  prdsex  13288  imasex  13324  fsumcncntop  15226  dvmptfsum  15384