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Theorem ax3h 38351
Description: Recovery of ax-3 8 from hirstL-ax3 38350. (Contributed by Jarvin Udandy, 3-Jul-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax3h  |-  ( ( -.  ph  ->  -.  ps )  ->  ( ps  ->  ph ) )

Proof of Theorem ax3h
StepHypRef Expression
1 hirstL-ax3 38350 . 2  |-  ( ( -.  ph  ->  -.  ps )  ->  ( ( -. 
ph  ->  ps )  ->  ph ) )
2 jarr 101 . 2  |-  ( ( ( -.  ph  ->  ps )  ->  ph )  -> 
( ps  ->  ph )
)
31, 2syl 17 1  |-  ( ( -.  ph  ->  -.  ps )  ->  ( ps  ->  ph ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-or 371
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator