Theorem stoic1b

Description: Stoic logic Thema 1 (part b). The other part of thema 1 of Stoic logic; see stoic1a . (Contributed by David A. Wheeler, 16-Feb-2019)

	Ref	Expression
Hypothesis	stoic1.1	$$⊢\left(\phi \wedge \psi \right)\to \theta$$
Assertion	stoic1b	$$⊢\left(\psi \wedge \neg \theta \right)\to \neg \phi$$

Proof

Step	Hyp	Ref	Expression
1		stoic1.1	$$⊢\left(\phi \wedge \psi \right)\to \theta$$
2	1	ancoms	$$⊢\left(\psi \wedge \phi \right)\to \theta$$
3	2	stoic1a	$$⊢\left(\psi \wedge \neg \theta \right)\to \neg \phi$$