Theorem intnanr

Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 3-Apr-1995)

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

Proof

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