Theorem euanv 2135

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 1572	. 2 |- ( ph -> A. x ph )
2	1	euan 2134	1 |- ( E! x ( ph /\ ps ) <-> ( ph /\ E! x ps ) )

Syntax hints:   /\ wa 104   <-> wb 105   E!weu 2077

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-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-eu 2080  df-mo 2081

This theorem is referenced by:  eueq2dc  2976  fsn  5807