Theorem 19.23 1656

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 1655	. 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 104   A.wal 1329   F/wnf 1436   E.wex 1468

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514  ax-i5r 1515

This theorem depends on definitions:  df-bi 116  df-nf 1437

This theorem is referenced by:  equsal  1705  r19.3rm  3446  ralidm  3458