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Theorem euorv 1972
Description: Introduce a disjunct into a unique existential 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 ax-17 1462 . 2  |-  ( ph  ->  A. x ph )
21euor 1971 1  |-  ( ( -.  ph  /\  E! x ps )  ->  E! x
( ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 102    \/ wo 662   E!weu 1945
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-17 1462  ax-ial 1470
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-fal 1293  df-eu 1948
This theorem is referenced by:  eueq2dc  2779
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