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Theorem ax6o 1725
Description: Show that the original axiom ax-6o 2079 can be derived from ax-6 1704 and others. See ax6 2088 for the rederivation of ax-6 1704 from ax-6o 2079.

Normally, ax6o 1725 should be used rather than ax-6o 2079, 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 sp 1717 . 2  |-  ( A. x ph  ->  ph )
2 ax-6 1704 . 2  |-  ( -. 
A. x ph  ->  A. x  -.  A. x ph )
31, 2nsyl4 134 1  |-  ( -. 
A. x  -.  A. x ph  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527
This theorem is referenced by:  hbnt  1726  equsalhw  1732  a6e  1757  nfnd  1762  modal-b  1781  ax9o  1892  hbntg  23566  ax4567  27012  hbntal  27602
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1636  ax-8 1644  ax-6 1704  ax-11 1716
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