Theorem csbeq2dv 3028

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 1508	. 2 |- F/ x ph
2		csbeq2dv.1	. 2 |- ( ph -> B = C )
3	1, 2	csbeq2d 3027	1 |- ( ph -> [_ A / x ]_ B = [_ A / x ]_ C )

Syntax hints:   -> wi 4   = wceq 1331   [_csb 3003

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 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-sbc 2910  df-csb 3004

This theorem is referenced by:  csbeq2i  3029  mpomptsx  6095  dmmpossx  6097  fmpox  6098  fmpoco  6113  fisumcom2  11207  fsumcncntop  12725