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Theorem ax6o 1735
Description: Show that the original axiom ax-6o 2089 can be derived from ax-6 1715 and others. See ax6 2099 for the rederivation of ax-6 1715 from ax-6o 2089.

Normally, ax6o 1735 should be used rather than ax-6o 2089, 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 1728 . 2  |-  ( A. x ph  ->  ph )
2 ax-6 1715 . 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 1530
This theorem is referenced by:  hbnt  1736  equsalhw  1742  a6e  1767  nfnd  1772  modal-b  1791  ax9o  1903  hbntg  24233  ax4567  27704  hbntal  28618  ax9oNEW7  29446
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
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