Theorem csbeq2dv 3075

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 1521	. 2 |- F/ x ph
2		csbeq2dv.1	. 2 |- ( ph -> B = C )
3	1, 2	csbeq2d 3074	1 |- ( ph -> [_ A / x ]_ B = [_ A / x ]_ C )

Syntax hints:   -> wi 4   = wceq 1348   [_csb 3049

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 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-sbc 2956  df-csb 3050

This theorem is referenced by:  csbeq2i  3076  mpomptsx  6176  dmmpossx  6178  fmpox  6179  fmpoco  6195  fisumcom2  11401  fprodcom2fi  11589  fsumcncntop  13350