Theorem stoic2b 1798

Description: Stoic logic Thema 2 version b. See stoic2a 1797. Version b is with the phrase "or both". We already have this rule as mpd3an3 1486, 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 1486	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 400   ∧ w3a 1101

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 210  df-an 401  df-3an 1103

This theorem is referenced by: (None)