Theorem euanv 2056

Description: Introduction of a conjunct into unique existential quantifier. (Contributed by NM, 23-Mar-1995.)

Assertion

Ref	Expression
euanv	|- ( E! x ( ph /\ ps ) <-> ( ph /\ E! x ps ) )

Distinct variable group:   ph, x

Allowed substitution hint:   ps( x)

Proof of Theorem euanv

Step	Hyp	Ref	Expression
1		ax-17 1506	. 2 |- ( ph -> A. x ph )
2	1	euan 2055	1 |- ( E! x ( ph /\ ps ) <-> ( ph /\ E! x ps ) )

Syntax hints:   /\ wa 103   <-> wb 104   E!weu 1999

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003

This theorem is referenced by:  eueq2dc  2857  fsn  5592