Theorem sbceq2a 2965

Description: Equality theorem for class substitution. Class version of sbequ12r 1765. (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 2964	. . 3 |- ( x = A -> ( ph <-> [. A / x ]. ph ) )
2	1	eqcoms 2173	. 2 |- ( A = x -> ( ph <-> [. A / x ]. ph ) )
3	2	bicomd 140	1 |- ( A = x -> ( [. A / x ]. ph <-> ph ) )

Syntax hints:   -> wi 4   <-> wb 104   = wceq 1348   [.wsbc 2955

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-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-sbc 2956

This theorem is referenced by: (None)