Users' Mathboxes Mathbox for Frédéric Liné < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  alneal2 Unicode version

Theorem alneal2 25104
Description: If  ph always holds, it always holds in the next step. (Contributed by FL, 20-Mar-2011.)
Assertion
Ref Expression
alneal2  |-  ( [.] ph  ->  () [.] ph )

Proof of Theorem alneal2
StepHypRef Expression
1 albineal 25102 . 2  |-  ( [.] ph 
<->  ( ph  /\  () [.] ph ) )
21simprbi 450 1  |-  ( [.] ph  ->  () [.] ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   [.]wbox 25073   ()wcirc 25075
This theorem is referenced by:  alne  25105  alalifal  25106
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ltl1 25077  ax-ltl2 25078  ax-ltl3 25079  ax-ltl4 25080  ax-lmp 25081  ax-nmp 25082  ax-ltl5 25096  ax-ltl6 25097
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-dia 25083
  Copyright terms: Public domain W3C validator