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Metamath Proof Explorer

Theorem intn3an2d

Description: Introduction of a triple conjunct inside a contradiction. (Contributed by FL, 27-Dec-2007) (Proof shortened by Andrew Salmon, 26-Jun-2011)

		Ref	Expression
	Hypothesis	intn3and.1	⊢ ( 𝜑 → ¬ 𝜓 )
	Assertion	intn3an2d	⊢ ( 𝜑 → ¬ ( 𝜒 ∧ 𝜓 ∧ 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		intn3and.1	⊢ ( 𝜑 → ¬ 𝜓 )
2		simp2	⊢ ( ( 𝜒 ∧ 𝜓 ∧ 𝜃 ) → 𝜓 )
3	1 2	nsyl	⊢ ( 𝜑 → ¬ ( 𝜒 ∧ 𝜓 ∧ 𝜃 ) )