Theorem 19.19 1659

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 1637	. 2 |- ( E. x ph <-> ph )
3		exbi 1597	. 2 |- ( A. x ( ph <-> ps ) -> ( E. x ph <-> E. x ps ) )
4	2, 3	bitr3id 193	1 |- ( A. x ( ph <-> ps ) -> ( ph <-> E. x ps ) )

Syntax hints:   -> wi 4   <-> wb 104   A.wal 1346   F/wnf 1453   E.wex 1485

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 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527

This theorem depends on definitions:  df-bi 116  df-nf 1454

This theorem is referenced by: (None)