Theorem euorv 2113

Description: Introduce a disjunct into a unique existential quantifier. (Contributed by NM, 23-Mar-1995.)

Assertion

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

Distinct variable group:   ph, x

Allowed substitution hint:   ps( x)

Proof of Theorem euorv

Step	Hyp	Ref	Expression
1		ax-17 1579	. 2 |- ( ph -> A. x ph )
2	1	euor 2112	1 |- ( ( -. ph /\ E! x ps ) -> E! x ( ph \/ ps ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 104   \/ wo 720   E!weu 2086

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-in1 623  ax-in2 624  ax-io 721  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-ial 1587

This theorem depends on definitions:  df-bi 117  df-tru 1405  df-fal 1408  df-eu 2089

This theorem is referenced by:  eueq2dc  2999