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Theorem stoic2b 1691
 Description: Stoic logic Thema 2 version b. See stoic2a 1690. Version b is with the phrase "or both". We already have this rule as mpd3an3 1417, 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 1417 1 ((𝜑𝜓) → 𝜃)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383   ∧ w3a 1031 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 196  df-an 385  df-3an 1033 This theorem is referenced by: (None)
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