MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  stoic4b Structured version   Visualization version   GIF version

Theorem stoic4b 1700
Description: Stoic logic Thema 4 version b. This is version b, which is with the phrase "or both". See stoic4a 1699 for more information. (Contributed by David A. Wheeler, 17-Feb-2019.)
Hypotheses
Ref Expression
stoic4b.1 ((𝜑𝜓) → 𝜒)
stoic4b.2 (((𝜒𝜑𝜓) ∧ 𝜃) → 𝜏)
Assertion
Ref Expression
stoic4b ((𝜑𝜓𝜃) → 𝜏)

Proof of Theorem stoic4b
StepHypRef Expression
1 stoic4b.1 . . 3 ((𝜑𝜓) → 𝜒)
213adant3 1079 . 2 ((𝜑𝜓𝜃) → 𝜒)
3 simp1 1059 . 2 ((𝜑𝜓𝜃) → 𝜑)
4 simp2 1060 . 2 ((𝜑𝜓𝜃) → 𝜓)
5 simp3 1061 . 2 ((𝜑𝜓𝜃) → 𝜃)
6 stoic4b.2 . 2 (((𝜒𝜑𝜓) ∧ 𝜃) → 𝜏)
72, 3, 4, 5, 6syl31anc 1326 1 ((𝜑𝜓𝜃) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1036
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1038
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator