MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  axc711 Unicode version

Theorem axc711 2244
Description: Proof of a single axiom that can replace both ax-c7 2216 and ax-11 1842. See axc711toc7 2246 and axc711to11 2247 for the re-derivation of those axioms. (Contributed by NM, 18-Nov-2006.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
axc711

Proof of Theorem axc711
StepHypRef Expression
1 ax-11 1842 . . . . 5
21con3i 135 . . . 4
32alimi 1633 . . 3
43con3i 135 . 2
5 ax-c7 2216 . 2
64, 5syl 16 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  A.wal 1393
This theorem is referenced by:  axc711toc7  2246  axc711to11  2247
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-11 1842  ax-c7 2216
  Copyright terms: Public domain W3C validator