Metamath Proof Explorer


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 → ¬ ( 𝜑𝜓 ) )

Proof

Step Hyp Ref Expression
1 simpl ( ( 𝜑𝜓 ) → 𝜑 )
2 1 con3i ( ¬ 𝜑 → ¬ ( 𝜑𝜓 ) )