Theorem 19.45 1613

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 1559	. 2 |- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )
2		19.45.1	. . . 4 |- F/ x ph
3	2	19.9 1575	. . 3 |- ( E. x ph <-> ph )
4	3	orbi1i 712	. 2 |- ( ( E. x ph \/ E. x ps ) <-> ( ph \/ E. x ps ) )
5	1, 4	bitri 182	1 |- ( E. x ( ph \/ ps ) <-> ( ph \/ E. x ps ) )

Syntax hints:   <-> wb 103   \/ wo 661   F/wnf 1389   E.wex 1421

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-nf 1390

This theorem is referenced by:  eeor  1625