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Theorem ax46 2114
Description: Proof of a single axiom that can replace ax-4 2087 and ax-6o 2089. See ax46to4 2115 and ax46to6 2116 for the re-derivation of those axioms. (Contributed by Scott Fenton, 12-Sep-2005.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax46  |-  ( ( A. x  -.  A. x ph  ->  A. x ph )  ->  ph )

Proof of Theorem ax46
StepHypRef Expression
1 ax-6o 2089 . 2  |-  ( -. 
A. x  -.  A. x ph  ->  ph )
2 ax-4 2087 . 2  |-  ( A. x ph  ->  ph )
31, 2ja 153 1  |-  ( ( A. x  -.  A. x ph  ->  A. x ph )  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530
This theorem is referenced by:  ax46to4  2115  ax46to6  2116
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-4 2087  ax-6o 2089
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