Metamath Proof Explorer

Theorem stoic3

Description: Stoic logic Thema 3. Statement T3 of Bobzien p. 116-117 discusses Stoic logic Thema 3. "When from two (assemblies) a third follows, and from the one that follows (i.e., the third) together with another, external assumption, another follows, then that other follows from the first two and the externally co-assumed one. (Simp. Cael. 237.2-4)" (Contributed by David A. Wheeler, 17-Feb-2019)

	Ref	Expression
Hypotheses	stoic3.1	$⊢ (φ \land ψ) \to χ$
	stoic3.2	$⊢ (χ \land θ) \to τ$
Assertion	stoic3	$⊢ (φ \land ψ \land θ) \to τ$

Proof

Step	Hyp	Ref	Expression
1		stoic3.1	$⊢ (φ \land ψ) \to χ$
2		stoic3.2	$⊢ (χ \land θ) \to τ$
3	1 2	sylan	$⊢ ((φ \land ψ) \land θ) \to τ$
4	3	3impa	$⊢ (φ \land ψ \land θ) \to τ$