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Theorem dedlem0a 918
Description: Lemma for an alternate version of weak deduction theorem. (Contributed by NM, 2-Apr-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)
Assertion
Ref Expression
dedlem0a  |-  ( ph  ->  ( ps  <->  ( ( ch  ->  ph )  ->  ( ps  /\  ph ) ) ) )

Proof of Theorem dedlem0a
StepHypRef Expression
1 iba 489 . 2  |-  ( ph  ->  ( ps  <->  ( ps  /\ 
ph ) ) )
2 ax-1 5 . . 3  |-  ( ph  ->  ( ch  ->  ph )
)
3 biimt 325 . . 3  |-  ( ( ch  ->  ph )  -> 
( ( ps  /\  ph )  <->  ( ( ch 
->  ph )  ->  ( ps  /\  ph ) ) ) )
42, 3syl 15 . 2  |-  ( ph  ->  ( ( ps  /\  ph )  <->  ( ( ch 
->  ph )  ->  ( ps  /\  ph ) ) ) )
51, 4bitrd 244 1  |-  ( ph  ->  ( ps  <->  ( ( ch  ->  ph )  ->  ( ps  /\  ph ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    /\ wa 358
This theorem is referenced by:  iftrue  3584
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
  Copyright terms: Public domain W3C validator