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Theorem speimfwALT 1804
Description: Alternate proof of speimfw 1803 (longer compressed proof, but fewer essential steps). (Contributed by NM, 23-Apr-2017.) (Proof shortened by Wolf Lammen, 5-Aug-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
speimfw.2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
speimfwALT  |-  ( -. 
A. x  -.  x  =  y  ->  ( A. x ph  ->  E. x ps ) )

Proof of Theorem speimfwALT
StepHypRef Expression
1 speimfw.2 . . 3  |-  ( x  =  y  ->  ( ph  ->  ps ) )
21eximi 1717 . 2  |-  ( E. x  x  =  y  ->  E. x ( ph  ->  ps ) )
3 df-ex 1674 . 2  |-  ( E. x  x  =  y  <->  -.  A. x  -.  x  =  y )
4 19.35 1750 . 2  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
52, 3, 43imtr3i 273 1  |-  ( -. 
A. x  -.  x  =  y  ->  ( A. x ph  ->  E. x ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1452   E.wex 1673
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692
This theorem depends on definitions:  df-bi 190  df-ex 1674
This theorem is referenced by: (None)
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