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Theorem ax67 2104
Description: Proof of a single axiom that can replace both ax-6o 2076 and ax-7 1708. See ax67to6 2106 and ax67to7 2107 for the re-derivation of those axioms. (Contributed by NM, 18-Nov-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax67  |-  ( -. 
A. x  -.  A. y A. x ph  ->  A. y ph )

Proof of Theorem ax67
StepHypRef Expression
1 ax-7 1708 . . . . 5  |-  ( A. y A. x ph  ->  A. x A. y ph )
21con3i 127 . . . 4  |-  ( -. 
A. x A. y ph  ->  -.  A. y A. x ph )
32alimi 1546 . . 3  |-  ( A. x  -.  A. x A. y ph  ->  A. x  -.  A. y A. x ph )
43con3i 127 . 2  |-  ( -. 
A. x  -.  A. y A. x ph  ->  -. 
A. x  -.  A. x A. y ph )
5 ax-6o 2076 . 2  |-  ( -. 
A. x  -.  A. x A. y ph  ->  A. y ph )
64, 5syl 15 1  |-  ( -. 
A. x  -.  A. y A. x ph  ->  A. y ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527
This theorem is referenced by:  ax67to6  2106  ax67to7  2107
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-7 1708  ax-6o 2076
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