Theorem euorv 1927

Description: Introduce a disjunct into a uniqueness 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 1419	. 2 |- ( ph -> A. x ph )
2	1	euor 1926	1 |- ( ( -. ph /\ E! x ps ) -> E! x ( ph \/ ps ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 97   \/ wo 629   E!weu 1900

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-eu 1903

This theorem is referenced by:  eueq2dc  2714