MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  hbn1 Structured version   Unicode version

Theorem hbn1 1889
Description: Alias for ax-10 1888 to be used instead of it. (Contributed by NM, 24-Jan-1993.) (Proof shortened by Wolf Lammen, 18-Aug-2014.)
Assertion
Ref Expression
hbn1  |-  ( -. 
A. x ph  ->  A. x  -.  A. x ph )

Proof of Theorem hbn1
StepHypRef Expression
1 ax-10 1888 1  |-  ( -. 
A. x ph  ->  A. x  -.  A. x ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1436
This theorem was proved from axioms:  ax-10 1888
This theorem is referenced by:  hbe1  1890  modal-5  1892  axc4  1912  axc7  1913  axc14  2167  ax12indn  32477  axc5c4c711  36654  vk15.4j  36787  ax6e2nd  36827  ax6e2ndVD  37210  ax6e2ndALT  37232
  Copyright terms: Public domain W3C validator