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Theorem expl 370
Description: Export a wff from a left conjunct. (Contributed by Jeff Hankins, 28-Aug-2009.)
Hypothesis
Ref Expression
expl.1  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
Assertion
Ref Expression
expl  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)

Proof of Theorem expl
StepHypRef Expression
1 expl.1 . . 3  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
21exp31 356 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32impd 251 1  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
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 is referenced by:  ssenen  6567  recclnq  6951  shftfvalg  10252  shftfval  10255  fsum2dlemstep  10828
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