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Theorem ax467 1752
 Description: Proof of a single axiom that can replace ax-4 1692, ax-6o 1697, and ax-7 1535 in a subsystem that includes these axioms plus ax-5o 1694 and ax-gen 1536 (and propositional calculus). See ax467to4 1753, ax467to6 1754, and ax467to7 1755 for the re-derivation of those axioms. This theorem extends the idea in Scott Fenton's ax46 1746. (Contributed by NM, 18-Nov-2006.) (Proof modification is discouraged.)
Assertion
Ref Expression
ax467

Proof of Theorem ax467
StepHypRef Expression
1 ax-4 1692 . . 3
2 hbn1 1564 . . . 4
3 ax-6o 1697 . . . . . 6
43con1i 123 . . . . 5
54alimi 1546 . . . 4
6 ax-7 1535 . . . 4
72, 5, 63syl 20 . . 3
81, 7nsyl4 136 . 2
9 ax-4 1692 . 2
108, 9ja 155 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6  wal 1532 This theorem is referenced by:  ax467to4  1753  ax467to6  1754  ax467to7  1755 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-4 1692  ax-6o 1697
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