ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  stoic2b GIF version

Theorem stoic2b 1360
Description: Stoic logic Thema 2 version b. See stoic2a 1359.

Version b is with the phrase "or both". We already have this rule as mpd3an3 1270, so here we prove the equivalence and discourage its use. (New usage is discouraged.) (Contributed by David A. Wheeler, 17-Feb-2019.)

Hypotheses
Ref Expression
stoic2b.1 ((𝜑𝜓) → 𝜒)
stoic2b.2 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
stoic2b ((𝜑𝜓) → 𝜃)

Proof of Theorem stoic2b
StepHypRef Expression
1 stoic2b.1 . 2 ((𝜑𝜓) → 𝜒)
2 stoic2b.2 . 2 ((𝜑𝜓𝜒) → 𝜃)
31, 2mpd3an3 1270 1 ((𝜑𝜓) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator