Theorem stoic1b 1776

Description: Stoic logic Thema 1 (part b). The other part of thema 1 of Stoic logic; see stoic1a 1775. (Contributed by David A. Wheeler, 16-Feb-2019.)

Hypothesis

Ref	Expression
stoic1.1	⊢ ((𝜑 ∧ 𝜓) → 𝜃)

Assertion

Ref	Expression
stoic1b	⊢ ((𝜓 ∧ ¬ 𝜃) → ¬ 𝜑)

Proof of Theorem stoic1b

Step	Hyp	Ref	Expression
1		stoic1.1	. . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜃)
2	1	ancoms 459	. 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜃)
3	2	stoic1a 1775	1 ⊢ ((𝜓 ∧ ¬ 𝜃) → ¬ 𝜑)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 396

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 397

This theorem is referenced by:  hashdomi  14095  hfext  34485