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Theorem ax4567to7 27595
 Description: Re-derivation of ax-7 1750 from ax4567 27591. Note that ax-7 1750 is not required for the re-derivation. (Contributed by Andrew Salmon, 14-Jul-2011.) (Proof modification is discouraged.)
Assertion
Ref Expression
ax4567to7

Proof of Theorem ax4567to7
StepHypRef Expression
1 ax-1 6 . . 3
212alimi 1570 . 2
3 ax4567to6 27594 . . . 4
43con4i 125 . . 3
5 pm2.21 103 . . . . . . 7
6 ax4567 27591 . . . . . . . 8
7 sp 1764 . . . . . . . 8
86, 7syl6 32 . . . . . . 7
95, 8syl 16 . . . . . 6
109alimi 1569 . . . . 5
11 ax4567to6 27594 . . . . 5
1210, 11nsyl4 137 . . . 4
1312alimi 1569 . . 3
144, 13syl 16 . 2
15 pm2.27 38 . . . 4
16 id 21 . . . 4
1715, 16mpg 1558 . . 3
18172alimi 1570 . 2
192, 14, 183syl 19 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1550 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762 This theorem depends on definitions:  df-bi 179  df-ex 1552  df-nf 1555
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