ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  anabsi5 Unicode version

Theorem anabsi5 546
Description: Absorption of antecedent into conjunction. (Contributed by NM, 11-Jun-1995.) (Proof shortened by Wolf Lammen, 18-Nov-2013.)
Hypothesis
Ref Expression
anabsi5.1  |-  ( ph  ->  ( ( ph  /\  ps )  ->  ch )
)
Assertion
Ref Expression
anabsi5  |-  ( (
ph  /\  ps )  ->  ch )

Proof of Theorem anabsi5
StepHypRef Expression
1 anabsi5.1 . . 3  |-  ( ph  ->  ( ( ph  /\  ps )  ->  ch )
)
21imp 122 . 2  |-  ( (
ph  /\  ( ph  /\ 
ps ) )  ->  ch )
32anabss5 545 1  |-  ( (
ph  /\  ps )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  anabsi6  547  anabsi8  549  3anidm12  1231  equsexd  1664  rspce  2717  phplem3g  6562  ltexprlemrl  7159  ltexprlemru  7161  dvdssq  11285
  Copyright terms: Public domain W3C validator