Theorem 19.19 2097

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 2072	. 2 |- ( E. x ph <-> ph )
3		exbi 1773	. 2 |- ( A. x ( ph <-> ps ) -> ( E. x ph <-> E. x ps ) )
4	2, 3	syl5bbr 274	1 |- ( A. x ( ph <-> ps ) -> ( ph <-> E. x ps ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   E.wex 1704   F/wnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)