Theorem 19.45 1693

Description: Theorem 19.45 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)

Hypothesis

Ref	Expression
19.45.1	|- F/ x ph

Assertion

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

Proof of Theorem 19.45

Step	Hyp	Ref	Expression
1		19.43 1638	. 2 |- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
2		19.45.1	. . . 4 |- F/ x ph
3	2	19.9 1654	. . 3 |- ( E. x ph <-> ph )
4	3	orbi1i 764	. 2 |- ( ( E. x ph \/ E. x ps ) <-> ( ph \/ E. x ps ) )
5	1, 4	bitri 184	1 |- ( E. x ( ph \/ ps ) <-> ( ph \/ E. x ps ) )

Syntax hints:   <-> wb 105   \/ wo 709   F/wnf 1470   E.wex 1502

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 1457  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-4 1520  ax-ial 1544

This theorem depends on definitions:  df-bi 117  df-nf 1471

This theorem is referenced by:  eeor  1705