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Theorem ax67to6 2243
Description: Re-derivation of ax-6o 2213 from ax67 2241. Note that ax-6o 2213 and ax-7 1749 are not used by the re-derivation. (Contributed by NM, 18-Nov-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax67to6  |-  ( -. 
A. x  -.  A. x ph  ->  ph )

Proof of Theorem ax67to6
StepHypRef Expression
1 hba1-o 2225 . . . . 5  |-  ( A. x ph  ->  A. x A. x ph )
21con3i 129 . . . 4  |-  ( -. 
A. x A. x ph  ->  -.  A. x ph )
32alimi 1568 . . 3  |-  ( A. x  -.  A. x A. x ph  ->  A. x  -.  A. x ph )
43con3i 129 . 2  |-  ( -. 
A. x  -.  A. x ph  ->  -.  A. x  -.  A. x A. x ph )
5 ax67 2241 . 2  |-  ( -. 
A. x  -.  A. x A. x ph  ->  A. x ph )
6 ax-4 2211 . 2  |-  ( A. x ph  ->  ph )
74, 5, 63syl 19 1  |-  ( -. 
A. x  -.  A. x ph  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1549
This theorem is referenced by:  ax67to7  2244
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-7 1749  ax-4 2211  ax-5o 2212  ax-6o 2213
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