Theorem 19.44 1572

Description: Theorem 19.44 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)

Hypothesis

Ref	Expression
19.44.1	|- F/ x ps

Assertion

Ref	Expression
19.44	|- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ ps ) )

Proof of Theorem 19.44

Step	Hyp	Ref	Expression
1		19.43 1519	. 2 |- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
2		19.44.1	. . . 4 |- F/ x ps
3	2	19.9 1535	. . 3 |- ( E. x ps <-> ps )
4	3	orbi2i 679	. 2 |- ( ( E. x ph \/ E. x ps ) <-> ( E. x ph \/ ps ) )
5	1, 4	bitri 173	1 |- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ ps ) )

Syntax hints:   <-> wb 98   \/ wo 629   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-io 630  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:  eeor  1585