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Theorem stoic2b 1365
 Description: Stoic logic Thema 2 version b. See stoic2a 1364. Version b is with the phrase "or both". We already have this rule as mpd3an3 1275, 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 1275 1 ((𝜑𝜓) → 𝜃)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 103   ∧ w3a 925 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107 This theorem depends on definitions:  df-bi 116  df-3an 927 This theorem is referenced by: (None)
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