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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	$⊢ (φ \land ψ) \to χ$
	stoic2b.2	$⊢ (φ \land ψ \land χ) \to θ$
Assertion	stoic2b	$⊢ (φ \land ψ) \to θ$

Proof

Step	Hyp	Ref	Expression
1		stoic2b.1	$⊢ (φ \land ψ) \to χ$
2		stoic2b.2	$⊢ (φ \land ψ \land χ) \to θ$
3	1 2	mpd3an3	$⊢ (φ \land ψ) \to θ$