Theorem euor 2231

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

Hypothesis

Ref	Expression
euor.1	|- F/xph

Assertion

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

Proof of Theorem euor

Step	Hyp	Ref	Expression
1		euor.1	. . . 4 |- F/xph
2	1	nfn 1793	. . 3 |- F/x -. ph
3		biorf 394	. . 3 |- (-. ph -> (ps <-> (ph \/ ps)))
4	2, 3	eubid 2211	. 2 |- (-. ph -> (E!xps <-> E!x(ph \/ ps)))
5	4	biimpa 470	1 |- ((-. ph /\ E!xps) -> E!x(ph \/ ps))

This proof depends on syntax axioms:  -. wn 3   -> wi 4   \/ wo 357   /\ wa 358   F/wnf 1544  E!weu 2204

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This proof depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-eu 2208

This theorem is used by:  euorv  2232