Theorem euor 2512

Description: Introduce a disjunct into a uniqueness quantifier. (Contributed by NM, 21-Oct-2005.)

Hypothesis

Ref	Expression
euor.1	|- F/ x ph

Assertion

Ref	Expression
euor	|- ( ( -. ph /\ E! x ps ) -> E! x ( ph \/ ps ) )

Proof of Theorem euor

Step	Hyp	Ref	Expression
1		euor.1	. . . 4 |- F/ x ph
2	1	nfn 1784	. . 3 |- F/ x -. ph
3		biorf 420	. . 3 |- ( -. ph -> ( ps <-> ( ph \/ ps ) ) )
4	2, 3	eubid 2488	. 2 |- ( -. ph -> ( E! x ps <-> E! x ( ph \/ ps ) ) )
5	4	biimpa 501	1 |- ( ( -. ph /\ E! x ps ) -> E! x ( ph \/ ps ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 383   /\ wa 384   F/wnf 1708   E!weu 2470

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-or 385  df-an 386  df-ex 1705  df-nf 1710  df-eu 2474

This theorem is referenced by:  euorv  2513