Theorem euor 1398

Description: Introduce a disjunct into a uniqueness quantifier.

Hypothesis

Ref	Expression
euor.1	|- (ph -> A.xph)

Assertion

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

Proof of Theorem euor

Step	Hyp	Ref	Expression
1		euor.1	. . . 4 |- (ph -> A.xph)
2	1	hbn 1004	. . 3 |- (-. ph -> A.x -. ph)
3		biorf 735	. . 3 |- (-. ph -> (ps <-> (ph \/ ps)))
4	2, 3	eubid 1385	. 2 |- (-. ph -> (E!xps <-> E!x(ph \/ ps)))
5	4	biimpa 416	1 |- ((-. ph /\ E!xps) -> E!x(ph \/ ps))

Syntax hints:  -. wn 2   -> wi 3   \/ wo 222   /\ wa 223  A.wal 954  E!weu 1380

This theorem is referenced by:  euorv 1399  euor2 1437

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-eu 1382

Copyright terms: Public domain