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Theorem ax6o 1696
Description: Show that the original axiom ax-6o 1697 can be derived from ax-6 1534 and others. See ax6 1698 for the rederivation of ax-6 1534 from ax-6o 1697.

Normally, ax6o 1696 should be used rather than ax-6o 1697, except by theorems specifically studying the latter's properties. (Contributed by NM, 21-May-2008.)

Assertion
Ref Expression
ax6o  |-  ( -. 
A. x  -.  A. x ph  ->  ph )

Proof of Theorem ax6o
StepHypRef Expression
1 ax-4 1692 . 2  |-  ( A. x ph  ->  ph )
2 ax-6 1534 . 2  |-  ( -. 
A. x ph  ->  A. x  -.  A. x ph )
31, 2nsyl4 136 1  |-  ( -. 
A. x  -.  A. x ph  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6   A.wal 1532
This theorem is referenced by:  a6e  1716  hbnt  1717  nfnd  1726  modal-b  1757  hbntal  27012
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-6 1534  ax-4 1692
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