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Metamath Proof Explorer

Theorem stoic2a

Description: Stoic logic Thema 2 version a. Statement T2 of Bobzien p. 117 shows a reconstructed version of Stoic logic thema 2 as follows: "When from two assertibles a third follows, and from the third and one (or both) of the two another follows, then this other follows from the first two." Bobzien uses constructs such as ph , ps |- ch ; in Metamath we will represent that construct as ph /\ ps -> ch . This version a is without the phrase "or both"; see stoic2b for the version with the phrase "or both". We already have this rule as syldan , so here we show the equivalence and discourage its use. (New usage is discouraged.) (Contributed by David A. Wheeler, 17-Feb-2019)

	Ref	Expression
Hypotheses	stoic2a.1	$⊢ (φ \land ψ) \to χ$
	stoic2a.2	$⊢ (φ \land χ) \to θ$
Assertion	stoic2a	$⊢ (φ \land ψ) \to θ$

Proof

Step	Hyp	Ref	Expression
1		stoic2a.1	$⊢ (φ \land ψ) \to χ$
2		stoic2a.2	$⊢ (φ \land χ) \to θ$
3	1 2	syldan	$⊢ (φ \land ψ) \to θ$