Theorem 19.19 1556

Description: Theorem 19.19 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)

Hypothesis

Ref	Expression
19.19.1	|- F/ x ph

Assertion

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

Proof of Theorem 19.19

Step	Hyp	Ref	Expression
1		19.19.1	. . 3 |- F/ x ph
2	1	19.9 1535	. 2 |- ( E. x ph <-> ph )
3		exbi 1495	. 2 |- ( A. x ( ph <-> ps ) -> ( E. x ph <-> E. x ps ) )
4	2, 3	syl5bbr 183	1 |- ( A. x ( ph <-> ps ) -> ( ph <-> E. x ps ) )

Syntax hints:   -> wi 4   <-> wb 98   A.wal 1241   F/wnf 1349   E.wex 1381

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 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-nf 1350

This theorem is referenced by: (None)