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Theorem ax6o 1725
Description: Show that the original axiom ax-6o 2078 can be derived from ax-6 1705 and others. See ax6 2088 for the rederivation of ax-6 1705 from ax-6o 2078.

Normally, ax6o 1725 should be used rather than ax-6o 2078, 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 1718 . 2  |-  ( A. x ph  ->  ph )
2 ax-6 1705 . 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 1529
This theorem is referenced by:  hbnt  1726  equsalhw  1732  a6e  1757  nfnd  1762  modal-b  1781  ax9o  1892  hbntg  24164  ax4567  27612  hbntal  28375
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-11 1717
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