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Theorem stoic2b 1440
Description: Stoic logic Thema 2 version b. See stoic2a 1439.

Version b is with the phrase "or both". We already have this rule as mpd3an3 1348, 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 1348 1 ((𝜑𝜓) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  w3a 979
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 981
This theorem is referenced by: (None)
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