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Theorem stoic4b 1779
 Description: Stoic logic Thema 4 version b. This is version b, which is with the phrase "or both". See stoic4a 1778 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 1128 . 2 ((𝜑𝜓𝜃) → 𝜒)
3 simp1 1132 . 2 ((𝜑𝜓𝜃) → 𝜑)
4 simp2 1133 . 2 ((𝜑𝜓𝜃) → 𝜓)
5 simp3 1134 . 2 ((𝜑𝜓𝜃) → 𝜃)
6 stoic4b.2 . 2 (((𝜒𝜑𝜓) ∧ 𝜃) → 𝜏)
72, 3, 4, 5, 6syl31anc 1369 1 ((𝜑𝜓𝜃) → 𝜏)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 398   ∧ w3a 1083 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 209  df-an 399  df-3an 1085 This theorem is referenced by: (None)
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