Theorem 19.44 1693

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 1639	. 2 |- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
2		19.44.1	. . . 4 |- F/ x ps
3	2	19.9 1655	. . 3 |- ( E. x ps <-> ps )
4	3	orbi2i 763	. 2 |- ( ( E. x ph \/ E. x ps ) <-> ( E. x ph \/ ps ) )
5	1, 4	bitri 184	1 |- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ ps ) )

Syntax hints:   <-> wb 105   \/ wo 709   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-io 710  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:  eeor  1706