Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  frege61a Structured version   Visualization version   GIF version

Theorem frege61a 37193
Description: Lemma for frege65a 37197. Proposition 61 of [Frege1879] p. 52. (Contributed by RP, 17-Apr-2020.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege61a ((if-(𝜑, 𝜓, 𝜒) → 𝜃) → ((𝜓𝜒) → 𝜃))

Proof of Theorem frege61a
StepHypRef Expression
1 ax-frege58a 37189 . 2 ((𝜓𝜒) → if-(𝜑, 𝜓, 𝜒))
2 frege9 37126 . 2 (((𝜓𝜒) → if-(𝜑, 𝜓, 𝜒)) → ((if-(𝜑, 𝜓, 𝜒) → 𝜃) → ((𝜓𝜒) → 𝜃)))
31, 2ax-mp 5 1 ((if-(𝜑, 𝜓, 𝜒) → 𝜃) → ((𝜓𝜒) → 𝜃))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  if-wif 1006
This theorem was proved from axioms:  ax-mp 5  ax-frege1 37104  ax-frege2 37105  ax-frege8 37123  ax-frege58a 37189
This theorem is referenced by:  frege65a  37197
  Copyright terms: Public domain W3C validator