Theorem bj-equsal1ti 32810

Description: Inference associated with bj-equsal1t 32809. (Contributed by BJ, 30-Sep-2018.)

Hypothesis

Ref	Expression
bj-equsal1ti.1	|- F/ x ph

Assertion

Ref	Expression
bj-equsal1ti	|- ( A. x ( x = y -> ph ) <-> ph )

Proof of Theorem bj-equsal1ti

Step	Hyp	Ref	Expression
1		bj-equsal1ti.1	. 2 |- F/ x ph
2		bj-equsal1t 32809	. 2 |- ( F/ x ph -> ( A. x ( x = y -> ph ) <-> ph ) )
3	1, 2	ax-mp 5	1 |- ( A. x ( x = y -> ph ) <-> ph )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   F/wnf 1708

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-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-nf 1710

This theorem is referenced by:  bj-equsal1  32811  bj-equsal2  32812