Theorem 19.19 1677

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 1655	. 2 |- ( E. x ph <-> ph )
3		exbi 1615	. 2 |- ( A. x ( ph <-> ps ) -> ( E. x ph <-> E. x ps ) )
4	2, 3	bitr3id 194	1 |- ( A. x ( ph <-> ps ) -> ( ph <-> E. x 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

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

This theorem is referenced by: (None)