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Theorem frege55lem2a 36433
Description: Core proof of Proposition 55 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege55lem2a  |-  ( (
ph 
<->  ps )  -> if- ( ps ,  ph ,  -.  ph ) )

Proof of Theorem frege55lem2a
StepHypRef Expression
1 bicom1 202 . . 3  |-  ( (
ph 
<->  ps )  ->  ( ps 
<-> 
ph ) )
2 frege54cor0a 36429 . . 3  |-  ( ( ps  <->  ph )  <-> if- ( ps ,  ph ,  -.  ph ) )
31, 2sylib 199 . 2  |-  ( (
ph 
<->  ps )  -> if- ( ps ,  ph ,  -.  ph ) )
43idi 2 1  |-  ( (
ph 
<->  ps )  -> if- ( ps ,  ph ,  -.  ph ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 187  if-wif 1420
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege28 36396
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-ifp 1421
This theorem is referenced by: (None)
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