Theorem csbeq2dv 3095

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 1538	. 2 |- F/ x ph
2		csbeq2dv.1	. 2 |- ( ph -> B = C )
3	1, 2	csbeq2d 3094	1 |- ( ph -> [_ A / x ]_ B = [_ A / x ]_ C )

Syntax hints:   -> wi 4   = wceq 1363   [_csb 3069

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 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-11 1516  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-sbc 2975  df-csb 3070

This theorem is referenced by:  csbeq2i  3096  mpomptsx  6212  dmmpossx  6214  fmpox  6215  fmpoco  6231  fisumcom2  11460  fprodcom2fi  11648  prdsex  12736  imasex  12744  fsumcncntop  14352