Theorem 3an1rs 1357

Description: Swap conjuncts. (Contributed by NM, 16-Dec-2007.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)

Hypothesis

Ref	Expression
3an1rs.1	⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜏)

Assertion

Ref	Expression
3an1rs	⊢ (((𝜑 ∧ 𝜓 ∧ 𝜃) ∧ 𝜒) → 𝜏)

Proof of Theorem 3an1rs

Step	Hyp	Ref	Expression
1		3an1rs.1	. . . 4 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜏)
2	1	3exp1 1350	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))
3	2	com34 91	. 2 ⊢ (𝜑 → (𝜓 → (𝜃 → (𝜒 → 𝜏))))
4	3	3imp1 1345	1 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜃) ∧ 𝜒) → 𝜏)

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:  odf1o2  19093  neiptopnei  22191  cnextcn  23126  nlpineqsn  35506  factwoffsmonot  40091