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Theorem pm4.71r 612
Description: Implication in terms of biconditional and conjunction. Theorem *4.71 of [WhiteheadRussell] p. 120 (with conjunct reversed). (Contributed by NM, 25-Jul-1999.)
Assertion
Ref Expression
pm4.71r  |-  ( (
ph  ->  ps )  <->  ( ph  <->  ( ps  /\  ph )
) )

Proof of Theorem pm4.71r
StepHypRef Expression
1 pm4.71 611 . 2  |-  ( (
ph  ->  ps )  <->  ( ph  <->  (
ph  /\  ps )
) )
2 ancom 437 . . 3  |-  ( (
ph  /\  ps )  <->  ( ps  /\  ph )
)
32bibi2i 304 . 2  |-  ( (
ph 
<->  ( ph  /\  ps ) )  <->  ( ph  <->  ( ps  /\  ph )
) )
41, 3bitri 240 1  |-  ( (
ph  ->  ps )  <->  ( ph  <->  ( ps  /\  ph )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  pm4.71ri  614  pm4.71rd  616
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
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