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Theorem pm4.45im 321
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 5 . . 3  |-  ( ph  ->  ( ps  ->  ph )
)
21ancli 310 . 2  |-  ( ph  ->  ( ph  /\  ( ps  ->  ph ) ) )
3 simpl 106 . 2  |-  ( (
ph  /\  ( ps  ->  ph ) )  ->  ph )
42, 3impbii 121 1  |-  ( ph  <->  (
ph  /\  ( ps  ->  ph ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101    <-> wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  difdif  3097
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