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Theorem ax6o 1723
Description: Show that the original axiom ax-6o 2076 can be derived from ax-6 1703 and others. See ax6 2086 for the rederivation of ax-6 1703 from ax-6o 2076.

Normally, ax6o 1723 should be used rather than ax-6o 2076, 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 1716 . 2  |-  ( A. x ph  ->  ph )
2 ax-6 1703 . 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  1724  equsalhw  1730  a6e  1755  nfnd  1760  modal-b  1779  ax9o  1890  hbntg  24162  ax4567  27601  hbntal  28319
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 1635  ax-8 1643  ax-6 1703  ax-11 1715
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