Theorem exnalim 1699

Description: One direction of Theorem 19.14 of [Margaris] p. 90. The converse holds in classical but not in intuitionistic logic. (Contributed by Jim Kingdon, 15-Jul-2018.)

Assertion

Ref	Expression
exnalim	|- ( E. x -. ph -> -. A. x ph )

Proof of Theorem exnalim

Step	Hyp	Ref	Expression
1		alexim 1698	. 2 |- ( A. x ph -> -. E. x -. ph )
2	1	con2i 636	1 |- ( E. x -. ph -> -. A. x ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1400   E.wex 1545

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 623  ax-in2 624  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-ial 1587

This theorem depends on definitions:  df-bi 117  df-tru 1405  df-fal 1408  df-nf 1514

This theorem is referenced by:  exanaliim  1700  alexnim  1701  nnal  1702  dtru  4705  brprcneu  5686