Theorem intnan

Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 16-Sep-1993)

	Ref	Expression
Hypothesis	intnan.1	⊢ ¬ 𝜑
Assertion	intnan	⊢ ¬ ( 𝜓 ∧ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		intnan.1	⊢ ¬ 𝜑
2		simpr	⊢ ( ( 𝜓 ∧ 𝜑 ) → 𝜑 )
3	1 2	mto	⊢ ¬ ( 𝜓 ∧ 𝜑 )