NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  ax467 Unicode version

Theorem ax467 2169
Description: Proof of a single axiom that can replace ax-4 2135, ax-6o 2137, and ax-7 1734 in a subsystem that includes these axioms plus ax-5o 2136 and ax-gen 1546 (and propositional calculus). See ax467to4 2170, ax467to6 2171, and ax467to7 2172 for the re-derivation of those axioms. This theorem extends the idea in Scott Fenton's ax46 2162. (Contributed by NM, 18-Nov-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax467

Proof of Theorem ax467
StepHypRef Expression
1 ax-4 2135 . . 3
2 ax6 2147 . . . 4
3 ax-6o 2137 . . . . . 6
43con1i 121 . . . . 5
54alimi 1559 . . . 4
6 ax-7 1734 . . . 4
72, 5, 63syl 18 . . 3
81, 7nsyl4 134 . 2
9 ax-4 2135 . 2
108, 9ja 153 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4  wal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-7 1734  ax-4 2135  ax-5o 2136  ax-6o 2137
This theorem is referenced by:  ax467to4  2170  ax467to6  2171  ax467to7  2172
  Copyright terms: Public domain W3C validator