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Theorem stoic4b 1322
 Description: Stoic logic Thema 4 version b. This is version b, which is with the phrase "or both". See stoic4a 1321 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 924 . 2 ((𝜑𝜓𝜃) → 𝜒)
3 simp1 904 . 2 ((𝜑𝜓𝜃) → 𝜑)
4 simp2 905 . 2 ((𝜑𝜓𝜃) → 𝜓)
5 simp3 906 . 2 ((𝜑𝜓𝜃) → 𝜃)
6 stoic4b.2 . 2 (((𝜒𝜑𝜓) ∧ 𝜃) → 𝜏)
72, 3, 4, 5, 6syl31anc 1138 1 ((𝜑𝜓𝜃) → 𝜏)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ∧ w3a 885 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101 This theorem depends on definitions:  df-bi 110  df-3an 887 This theorem is referenced by: (None)
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