Theorem stoic2b 1779

Description: Stoic logic Thema 2 version b. See stoic2a 1778. Version b is with the phrase "or both". We already have this rule as mpd3an3 1460, 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 1460	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1085

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 396  df-3an 1087

This theorem is referenced by: (None)