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Theorem stoic4b 1338
Description: Stoic logic Thema 4 version b.

This is version b, which is with the phrase "or both". See stoic4a 1337 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 935 . 2 ((𝜑𝜓𝜃) → 𝜒)
3 simp1 915 . 2 ((𝜑𝜓𝜃) → 𝜑)
4 simp2 916 . 2 ((𝜑𝜓𝜃) → 𝜓)
5 simp3 917 . 2 ((𝜑𝜓𝜃) → 𝜃)
6 stoic4b.2 . 2 (((𝜒𝜑𝜓) ∧ 𝜃) → 𝜏)
72, 3, 4, 5, 6syl31anc 1149 1 ((𝜑𝜓𝜃) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by: (None)
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