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Theorem ax6o 1767
Description: Show that the original axiom ax-6o 2216 can be derived from ax-6 1745 and others. See ax6 2226 for the rederivation of ax-6 1745 from ax-6o 2216.

Normally, ax6o 1767 should be used rather than ax-6o 2216, 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 1764 . 2  |-  ( A. x ph  ->  ph )
2 ax-6 1745 . 2  |-  ( -. 
A. x ph  ->  A. x  -.  A. x ph )
31, 2nsyl4 137 1  |-  ( -. 
A. x  -.  A. x ph  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1550
This theorem is referenced by:  a6e  1768  modal-b  1769  hbntOLD  1801  nfndOLD  1811  equsalhwOLD  1862  ax9o  1955  hbntg  25435  ax4567  27580  hbntal  28702  ax9oNEW7  29531
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-ex 1552
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