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Theorem ax67to7 2120
Description: Re-derivation of ax-7 1720 from ax67 2117. Note that ax-6o 2089 and ax-7 1720 are not used by the re-derivation. (Contributed by NM, 18-Nov-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax67to7  |-  ( A. x A. y ph  ->  A. y A. x ph )

Proof of Theorem ax67to7
StepHypRef Expression
1 ax67to6 2119 . . 3  |-  ( -. 
A. y  -.  A. y  -.  A. x A. y ph  ->  -.  A. x A. y ph )
21con4i 122 . 2  |-  ( A. x A. y ph  ->  A. y  -.  A. y  -.  A. x A. y ph )
3 ax67 2117 . . 3  |-  ( -. 
A. y  -.  A. x A. y ph  ->  A. x ph )
43alimi 1549 . 2  |-  ( A. y  -.  A. y  -. 
A. x A. y ph  ->  A. y A. x ph )
52, 4syl 15 1  |-  ( A. x A. y ph  ->  A. y A. x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-7 1720  ax-4 2087  ax-5o 2088  ax-6o 2089
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