ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  exp4b Unicode version

Theorem exp4b 364
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.) (Proof shortened by Wolf Lammen, 23-Nov-2012.)
Hypothesis
Ref Expression
exp4b.1  |-  ( (
ph  /\  ps )  ->  ( ( ch  /\  th )  ->  ta )
)
Assertion
Ref Expression
exp4b  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )

Proof of Theorem exp4b
StepHypRef Expression
1 exp4b.1 . . 3  |-  ( (
ph  /\  ps )  ->  ( ( ch  /\  th )  ->  ta )
)
21ex 114 . 2  |-  ( ph  ->  ( ps  ->  (
( ch  /\  th )  ->  ta ) ) )
32exp4a 363 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  exp43  369  reuss2  3326  nndi  6350  mulnqprl  7344  mulnqpru  7345  distrlem5prl  7362  distrlem5pru  7363  recexprlemss1l  7411  recexprlemss1u  7412  lemul12a  8588  nnmulcl  8709  elfz0fzfz0  9871  fzo1fzo0n0  9928  fzofzim  9933  elfzodifsumelfzo  9946  le2sq2  10336  oddprmgt2  11741
  Copyright terms: Public domain W3C validator