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Theorem 2eu2ex 2037
Description: Double existential uniqueness. (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2eu2ex  |-  ( E! x E! y ph  ->  E. x E. y ph )

Proof of Theorem 2eu2ex
StepHypRef Expression
1 euex 1978 . 2  |-  ( E! x E! y ph  ->  E. x E! y
ph )
2 euex 1978 . . 3  |-  ( E! y ph  ->  E. y ph )
32eximi 1536 . 2  |-  ( E. x E! y ph  ->  E. x E. y ph )
41, 3syl 14 1  |-  ( E! x E! y ph  ->  E. x E. y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1426   E!weu 1948
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-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-eu 1951
This theorem is referenced by: (None)
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