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Theorem imp4b 342
Description: An importation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
imp4.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Assertion
Ref Expression
imp4b  |-  ( (
ph  /\  ps )  ->  ( ( ch  /\  th )  ->  ta )
)

Proof of Theorem imp4b
StepHypRef Expression
1 imp4.1 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
21imp4a 341 . 2  |-  ( ph  ->  ( ps  ->  (
( ch  /\  th )  ->  ta ) ) )
32imp 122 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:  imp43  347  ltmpig  6591  bndndx  8354
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