MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  euanv Structured version   Visualization version   Unicode version

Theorem euanv 2373
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
StepHypRef Expression
1 nfv 1771 . 2  |-  F/ x ph
21euan 2369 1  |-  ( E! x ( ph  /\  ps )  <->  ( ph  /\  E! x ps ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 189    /\ wa 375   E!weu 2309
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-10 1925  ax-12 1943
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1674  df-nf 1678  df-eu 2313
This theorem is referenced by:  eueq2  3223  2reu5lem1  3256  fsn  6084  dfac5lem5  8583
  Copyright terms: Public domain W3C validator