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Theorem exp43 364
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
exp43.1  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  ->  ta )
Assertion
Ref Expression
exp43  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )

Proof of Theorem exp43
StepHypRef Expression
1 exp43.1 . . 3  |-  ( ( ( ph  /\  ps )  /\  ( ch  /\  th ) )  ->  ta )
21ex 113 . 2  |-  ( (
ph  /\  ps )  ->  ( ( ch  /\  th )  ->  ta )
)
32exp4b 359 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
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:  exp53  369  funssres  4972  fvopab3ig  5278  fvmptt  5294  tfri3  6016  nnmordi  6155  ordiso2  6505  qaddcl  8801  qmulcl  8803  bernneq  9690
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