Theorem sbceq2a 2825

Description: Equality theorem for class substitution. Class version of sbequ12r 1695. (Contributed by NM, 4-Jan-2017.)

Assertion

Ref	Expression
sbceq2a	|- ( A = x -> ( [. A / x ]. ph <-> ph ) )

Proof of Theorem sbceq2a

Step	Hyp	Ref	Expression
1		sbceq1a 2824	. . 3 |- ( x = A -> ( ph <-> [. A / x ]. ph ) )
2	1	eqcoms 2084	. 2 |- ( A = x -> ( ph <-> [. A / x ]. ph ) )
3	2	bicomd 139	1 |- ( A = x -> ( [. A / x ]. ph <-> ph ) )

Syntax hints:   -> wi 4   <-> wb 103   = wceq 1284   [.wsbc 2815

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-sbc 2816

This theorem is referenced by: (None)