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Theorem ax46 1746
Description: Proof of a single axiom that can replace ax-4 1692 and ax-6o 1697. See ax46to4 1747 and ax46to6 1748 for the re-derivation of those axioms. (Contributed by Scott Fenton, 12-Sep-2005.) (Proof modification is discouraged.)
Assertion
Ref Expression
ax46  |-  ( ( A. x  -.  A. x ph  ->  A. x ph )  ->  ph )

Proof of Theorem ax46
StepHypRef Expression
1 ax-6o 1697 . 2  |-  ( -. 
A. x  -.  A. x ph  ->  ph )
2 ax-4 1692 . 2  |-  ( A. x ph  ->  ph )
31, 2ja 155 1  |-  ( ( A. x  -.  A. x ph  ->  A. x ph )  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6   A.wal 1532
This theorem is referenced by:  ax46to4  1747  ax46to6  1748
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-4 1692  ax-6o 1697
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