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Theorem hbe1a 2003
Description: Dual statement of hbe1 1475. (Contributed by Wolf Lammen, 15-Sep-2021.)
Assertion
Ref Expression
hbe1a  |-  ( E. x A. x ph  ->  A. x ph )

Proof of Theorem hbe1a
StepHypRef Expression
1 nfa1 1521 . . 3  |-  F/ x A. x ph
2 nf3 1649 . . 3  |-  ( F/ x A. x ph  <->  A. x ( E. x A. x ph  ->  A. x ph ) )
31, 2mpbi 144 . 2  |-  A. x
( E. x A. x ph  ->  A. x ph )
43spi 1516 1  |-  ( E. x A. x ph  ->  A. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1333   F/wnf 1440   E.wex 1472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-4 1490  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-nf 1441
This theorem is referenced by:  nf5-1  2004
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