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Theorem pm4.45im 547
Description: Conjunction with implication. Compare Theorem *4.45 of [WhiteheadRussell] p. 119. (Contributed by NM, 17-May-1998.)
Assertion
Ref Expression
pm4.45im  |-  ( ph  <->  (
ph  /\  ( ps  ->  ph ) ) )

Proof of Theorem pm4.45im
StepHypRef Expression
1 ax-1 7 . . 3  |-  ( ph  ->  ( ps  ->  ph )
)
21ancli 536 . 2  |-  ( ph  ->  ( ph  /\  ( ps  ->  ph ) ) )
3 simpl 445 . 2  |-  ( (
ph  /\  ( ps  ->  ph ) )  ->  ph )
42, 3impbii 182 1  |-  ( ph  <->  (
ph  /\  ( ps  ->  ph ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178    /\ wa 360
This theorem is referenced by:  difdif  3277
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-an 362
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