This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem 3imp21

Description: The importation inference 3imp with commutation of the first and second conjuncts of the assertion relative to the hypothesis. (Contributed by Alan Sare, 11-Sep-2016) (Revised to shorten 3com12 by Wolf Lammen, 23-Jun-2022.)

		Ref	Expression
	Hypothesis	3imp.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
	Assertion	3imp21	⊢ ( ( 𝜓 ∧ 𝜑 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		3imp.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2	1	com13	⊢ ( 𝜒 → ( 𝜓 → ( 𝜑 → 𝜃 ) ) )
3	2	3imp231	⊢ ( ( 𝜓 ∧ 𝜑 ∧ 𝜒 ) → 𝜃 )