Theorem axfrege52c 38181

Description: Justification for ax-frege52c 38182. (Contributed by RP, 24-Dec-2019.)

Assertion

Ref	Expression
axfrege52c	|- ( A = B -> ( [. A / x ]. ph -> [. B / x ]. ph ) )

Proof of Theorem axfrege52c

Step	Hyp	Ref	Expression
1		dfsbcq 3437	. 2 |- ( A = B -> ( [. A / x ]. ph <-> [. B / x ]. ph ) )
2	1	biimpd 219	1 |- ( A = B -> ( [. A / x ]. ph -> [. B / x ]. ph ) )

Syntax hints:   -> wi 4   = wceq 1483   [.wsbc 3435

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-cleq 2615  df-clel 2618  df-sbc 3436

This theorem is referenced by: (None)