Theorem euanv 2534

Description: Introduction of a conjunct into uniqueness 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		nfv 1843	. 2 |- F/ x ph
2	1	euan 2530	1 |- ( E! x ( ph /\ ps ) <-> ( ph /\ E! x ps ) )

Syntax hints:   <-> wb 196   /\ wa 384   E!weu 2470

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-eu 2474

This theorem is referenced by:  eueq2  3380  2reu5lem1  3413  fsn  6402  dfac5lem5  8950