Metamath Proof Explorer


Theorem stoic2b

Description: Stoic logic Thema 2 version b. See stoic2a . Version b is with the phrase "or both". We already have this rule as mpd3an3 , so here we prove the equivalence and discourage its use. (New usage is discouraged.) (Contributed by David A. Wheeler, 17-Feb-2019)

Ref Expression
Hypotheses stoic2b.1 ( ( 𝜑𝜓 ) → 𝜒 )
stoic2b.2 ( ( 𝜑𝜓𝜒 ) → 𝜃 )
Assertion stoic2b ( ( 𝜑𝜓 ) → 𝜃 )

Proof

Step Hyp Ref Expression
1 stoic2b.1 ( ( 𝜑𝜓 ) → 𝜒 )
2 stoic2b.2 ( ( 𝜑𝜓𝜒 ) → 𝜃 )
3 1 2 mpd3an3 ( ( 𝜑𝜓 ) → 𝜃 )