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Theorem euorv 2171
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 1605 . 2  |-  F/ x ph
21euor 2170 1  |-  ( ( -.  ph  /\  E! x ps )  ->  E! x
( ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 357    /\ wa 358   E!weu 2143
This theorem is referenced by:  eueq2  2939
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-eu 2147
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