Theorem sbceq2a 2996

Description: Equality theorem for class substitution. Class version of sbequ12r 1783. (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 2995	. . 3 |- ( x = A -> ( ph <-> [. A / x ]. ph ) )
2	1	eqcoms 2196	. 2 |- ( A = x -> ( ph <-> [. A / x ]. ph ) )
3	2	bicomd 141	1 |- ( A = x -> ( [. A / x ]. ph <-> ph ) )

Syntax hints:   -> wi 4   <-> wb 105   = wceq 1364   [.wsbc 2985

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-sbc 2986

This theorem is referenced by:  uchoice  6190