Theorem sbceq2a 2768

Description: Equality theorem for class substitution. Class version of sbequ12r 1652. (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 2767	. . 3 |- (x = A -> (ph <-> [.A / x ].ph))
2	1	eqcoms 2040	. 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 1242   [.wsbc 2758

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 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019

This theorem depends on definitions:  df-bi 110  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-sbc 2759

This theorem is referenced by: (None)