Theorem sbceq2a 2923

Description: Equality theorem for class substitution. Class version of sbequ12r 1746. (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 2922	. . 3 |- ( x = A -> ( ph <-> [. A / x ]. ph ) )
2	1	eqcoms 2143	. 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 1332   [.wsbc 2913

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 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-sbc 2914

This theorem is referenced by: (None)