Theorem pm3.2an3 1233

Description: Version of pm3.2 462 for a triple conjunction. (Contributed by Alan Sare, 24-Oct-2011.) (Proof shortened by Kyle Wyonch, 24-Apr-2021.)

Assertion

Ref	Expression
pm3.2an3	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜑 ∧ 𝜓 ∧ 𝜒))))

Proof of Theorem pm3.2an3

Step	Hyp	Ref	Expression
1		df-3an 1033	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒))
2	1	biimpri 217	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → (𝜑 ∧ 𝜓 ∧ 𝜒))
3	2	exp31 628	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜑 ∧ 𝜓 ∧ 𝜒))))

Syntax hints:   → wi 4   ∧ wa 383   ∧ w3a 1031

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 196  df-an 385  df-3an 1033

This theorem is referenced by:  3exp  1256  tratrb  37767  19.21a3con13vVD  38109  tratrbVD  38119