ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ancl Unicode version

Theorem ancl 311
Description: Conjoin antecedent to left of consequent. (Contributed by NM, 15-Aug-1994.)
Assertion
Ref Expression
ancl  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ph  /\ 
ps ) ) )

Proof of Theorem ancl
StepHypRef Expression
1 pm3.2 137 . 2  |-  ( ph  ->  ( ps  ->  ( ph  /\  ps ) ) )
21a2i 11 1  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ( ph  /\ 
ps ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-2 6  ax-mp 7  ax-ia3 106
This theorem is referenced by:  equs4  1657  eupickbi  2027
  Copyright terms: Public domain W3C validator