Theorem 3an1rs

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

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

Proof

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