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	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
	stoic2b.2	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	stoic2b	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		stoic2b.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
2		stoic2b.2	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
3	1 2	mpd3an3	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )