Theorem euanv 2111

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 1549	. 2 |- ( ph -> A. x ph )
2	1	euan 2110	1 |- ( E! x ( ph /\ ps ) <-> ( ph /\ E! x ps ) )

Syntax hints:   /\ wa 104   <-> wb 105   E!weu 2054

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-eu 2057  df-mo 2058

This theorem is referenced by:  eueq2dc  2946  fsn  5752