Theorem intnanrt

Description: Introduction of conjunct inside of a contradiction. Would be used in elfvov1 . (Contributed by SN, 18-May-2025)

	Ref	Expression
Assertion	intnanrt	⊢ ( ¬ 𝜑 → ¬ ( 𝜑 ∧ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		simpl	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜑 )
2	1	con3i	⊢ ( ¬ 𝜑 → ¬ ( 𝜑 ∧ 𝜓 ) )