Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  frege55lem2a Structured version   Visualization version   GIF version

Theorem frege55lem2a 37181
Description: Core proof of Proposition 55 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege55lem2a ((𝜑𝜓) → if-(𝜓, 𝜑, ¬ 𝜑))

Proof of Theorem frege55lem2a
StepHypRef Expression
1 bicom1 210 . . 3 ((𝜑𝜓) → (𝜓𝜑))
2 frege54cor0a 37177 . . 3 ((𝜓𝜑) ↔ if-(𝜓, 𝜑, ¬ 𝜑))
31, 2sylib 207 . 2 ((𝜑𝜓) → if-(𝜓, 𝜑, ¬ 𝜑))
43idi 2 1 ((𝜑𝜓) → if-(𝜓, 𝜑, ¬ 𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 195  if-wif 1006
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege28 37144
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-ifp 1007
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator