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Theorem impl 375
Description: Export a wff from a left conjunct. (Contributed by Mario Carneiro, 9-Jul-2014.)
Hypothesis
Ref Expression
impl.1  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
Assertion
Ref Expression
impl  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )

Proof of Theorem impl
StepHypRef Expression
1 impl.1 . . 3  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
21expd 256 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32imp31 254 1  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
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 is referenced by:  sbc2iedv  2951  csbie2t  3016  foco2  5621  erth  6439  distrlem1prl  7354  distrlem1pru  7355  uz11  9300  divgcdcoprm0  11689  cncongr1  11691
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