Theorem stoic2b 1778

Description: Stoic logic Thema 2 version b. See stoic2a 1777. Version b is with the phrase "or both". We already have this rule as mpd3an3 1461, so here we prove the equivalence and discourage its use. (New usage is discouraged.) (Contributed by David A. Wheeler, 17-Feb-2019.)

Hypotheses

Ref	Expression
stoic2b.1	⊢ ((𝜑 ∧ 𝜓) → 𝜒)
stoic2b.2	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
stoic2b	⊢ ((𝜑 ∧ 𝜓) → 𝜃)

Proof of Theorem stoic2b

Step	Hyp	Ref	Expression
1		stoic2b.1	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
2		stoic2b.2	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
3	1, 2	mpd3an3 1461	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 396   ∧ w3a 1086

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  df-3an 1088

This theorem is referenced by: (None)