Metamath Proof Explorer


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 )