Theorem stoic2b 1359

Description: Stoic logic Thema 2 version b. See stoic2a 1358.

Version b is with the phrase "or both". We already have this rule as mpd3an3 1269, 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 1269	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 102   ∧ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by: (None)