Theorem intnanrd

Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 10-Jul-2005)

	Ref	Expression
Hypothesis	intnand.1	⊢ ( 𝜑 → ¬ 𝜓 )
Assertion	intnanrd	⊢ ( 𝜑 → ¬ ( 𝜓 ∧ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		intnand.1	⊢ ( 𝜑 → ¬ 𝜓 )
2		simpl	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜓 )
3	1 2	nsyl	⊢ ( 𝜑 → ¬ ( 𝜓 ∧ 𝜒 ) )