Theorem sbceq2a 2774

Description: Equality theorem for class substitution. Class version of sbequ12r 1655. (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 2773	. . 3 |- ( x = A -> ( ph <-> [. A / x ]. ph ) )
2	1	eqcoms 2043	. 2 |- ( A = x -> ( ph <-> [. A / x ]. ph ) )
3	2	bicomd 129	1 |- ( A = x -> ( [. A / x ]. ph <-> ph ) )

Syntax hints:   -> wi 4   <-> wb 98   = wceq 1243   [.wsbc 2764

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-sbc 2765

This theorem is referenced by: (None)