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Theorem axc5c711toc7 32503
Description: Re-derivation of ax-c7 32469 from axc5c711 32501. Note that ax-c7 32469 and ax-11 1922 are not used by the re-derivation. The use of alimi 1686 (which uses ax-c5 32467) is allowed since we have already proved axc5c711toc5 32502. (Contributed by NM, 19-Nov-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
axc5c711toc7  |-  ( -. 
A. x  -.  A. x ph  ->  ph )

Proof of Theorem axc5c711toc7
StepHypRef Expression
1 hba1-o 32481 . . . . . 6  |-  ( A. x ph  ->  A. x A. x ph )
21con3i 141 . . . . 5  |-  ( -. 
A. x A. x ph  ->  -.  A. x ph )
32alimi 1686 . . . 4  |-  ( A. x  -.  A. x A. x ph  ->  A. x  -.  A. x ph )
43sps-o 32491 . . 3  |-  ( A. x A. x  -.  A. x A. x ph  ->  A. x  -.  A. x ph )
54con3i 141 . 2  |-  ( -. 
A. x  -.  A. x ph  ->  -.  A. x A. x  -.  A. x A. x ph )
6 pm2.21 112 . 2  |-  ( -. 
A. x A. x  -.  A. x A. x ph  ->  ( A. x A. x  -.  A. x A. x ph  ->  A. x ph ) )
7 axc5c711 32501 . 2  |-  ( ( A. x A. x  -.  A. x A. x ph  ->  A. x ph )  ->  ph )
85, 6, 73syl 18 1  |-  ( -. 
A. x  -.  A. x ph  ->  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1444
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-11 1922  ax-c5 32467  ax-c4 32468  ax-c7 32469
This theorem is referenced by:  axc5c711to11  32504
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