Theorem 19.23 1689

Description: Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)

Hypothesis

Ref	Expression
19.23.1	|- F/ x ps

Assertion

Ref	Expression
19.23	|- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )

Proof of Theorem 19.23

Step	Hyp	Ref	Expression
1		19.23.1	. 2 |- F/ x ps
2		19.23t 1688	. 2 |- ( F/ x ps -> ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) ) )
3	1, 2	ax-mp 5	1 |- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )

Syntax hints:   -> wi 4   <-> wb 105   A.wal 1362   F/wnf 1471   E.wex 1503

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-4 1521  ax-ial 1545  ax-i5r 1546

This theorem depends on definitions:  df-bi 117  df-nf 1472

This theorem is referenced by:  equsal  1738  equsalv  1804  r19.3rm  3526  ralidm  3538