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Theorem axc5c4c711toc4 36606
Description: Re-derivation of axc4 1910 from axc5c4c711 36604. Note that only propositional calculus is required for the re-derivation. (Contributed by Andrew Salmon, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
axc5c4c711toc4  |-  ( A. x ( A. x ph  ->  ps )  -> 
( A. x ph  ->  A. x ps )
)

Proof of Theorem axc5c4c711toc4
StepHypRef Expression
1 ax-1 6 . 2  |-  ( A. x ( A. x ph  ->  ps )  -> 
( ph  ->  A. x
( A. x ph  ->  ps ) ) )
2 ax-1 6 . 2  |-  ( (
ph  ->  A. x ( A. x ph  ->  ps )
)  ->  ( A. x A. x  -.  A. x A. x ( A. x ph  ->  ps )  ->  ( ph  ->  A. x
( A. x ph  ->  ps ) ) ) )
3 axc5c4c711 36604 . 2  |-  ( ( A. x A. x  -.  A. x A. x
( A. x ph  ->  ps )  ->  ( ph  ->  A. x ( A. x ph  ->  ps )
) )  ->  ( A. x ph  ->  A. x ps ) )
41, 2, 33syl 18 1  |-  ( A. x ( A. x ph  ->  ps )  -> 
( A. x ph  ->  A. x ps )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904
This theorem depends on definitions:  df-bi 188  df-ex 1660
This theorem is referenced by: (None)
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