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	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )
Assertion	stoic1b	⊢ ( ( 𝜓 ∧ ¬ 𝜃 ) → ¬ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		stoic1.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )
2	1	ancoms	⊢ ( ( 𝜓 ∧ 𝜑 ) → 𝜃 )
3	2	stoic1a	⊢ ( ( 𝜓 ∧ ¬ 𝜃 ) → ¬ 𝜑 )