Theorem stoic2b 1776

Description: Stoic logic Thema 2 version b. See stoic2a 1775. Version b is with the phrase "or both". We already have this rule as mpd3an3 1458, 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 1458	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 398   ∧ w3a 1083

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 209  df-an 399  df-3an 1085

This theorem is referenced by: (None)