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

Theorem embantd 55
Description: Deduction embedding an antecedent. (Contributed by Wolf Lammen, 4-Oct-2013.)
Hypotheses
Ref Expression
embantd.1  |-  ( ph  ->  ps )
embantd.2  |-  ( ph  ->  ( ch  ->  th )
)
Assertion
Ref Expression
embantd  |-  ( ph  ->  ( ( ps  ->  ch )  ->  th )
)

Proof of Theorem embantd
StepHypRef Expression
1 embantd.1 . 2  |-  ( ph  ->  ps )
2 embantd.2 . . 3  |-  ( ph  ->  ( ch  ->  th )
)
32imim2d 53 . 2  |-  ( ph  ->  ( ( ps  ->  ch )  ->  ( ps  ->  th ) ) )
41, 3mpid 41 1  |-  ( ph  ->  ( ( ps  ->  ch )  ->  th )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  a2and  525  el  4005  findcard2d  6587  findcard2sd  6588  exprmfct  11212  sqrt2irr  11234  bj-exlimmp  11327
  Copyright terms: Public domain W3C validator