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

Theorem euorv 2311
Description: Introduce a disjunct into a uniqueness quantifier. (Contributed by NM, 23-Mar-1995.)
Assertion
Ref Expression
euorv  |-  ( ( -.  ph  /\  E! x ps )  ->  E! x
( ph  \/  ps ) )
Distinct variable group:    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem euorv
StepHypRef Expression
1 nfv 1630 . 2  |-  F/ x ph
21euor 2310 1  |-  ( ( -.  ph  /\  E! x ps )  ->  E! x
( ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 359    /\ wa 360   E!weu 2283
This theorem is referenced by:  eueq2  3110
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-eu 2287
  Copyright terms: Public domain W3C validator