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Theorem pm4.45im 562
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 6 . . 3  |-  ( ph  ->  ( ps  ->  ph )
)
21ancli 551 . 2  |-  ( ph  ->  ( ph  /\  ( ps  ->  ph ) ) )
3 simpl 457 . 2  |-  ( (
ph  /\  ( ps  ->  ph ) )  ->  ph )
42, 3impbii 188 1  |-  ( ph  <->  (
ph  /\  ( ps  ->  ph ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  difdif  3630
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