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Metamath Proof Explorer

Theorem pm3.2an3

Description: Version of pm3.2 for a triple conjunction. (Contributed by Alan Sare, 24-Oct-2011) (Proof shortened by Kyle Wyonch, 24-Apr-2021) (Proof shortened by Wolf Lammen, 21-Jun-2022)

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

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) )
2	1	3exp	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) ) )