Theorem intnanrt 42193

Description: Introduction of conjunct inside of a contradiction. Would be used in elfvov1 7485. (Contributed by SN, 18-May-2025.)

Assertion

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

Proof of Theorem intnanrt

Step	Hyp	Ref	Expression
1		simpl 482	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
2	1	con3i 154	1 ⊢ (¬ 𝜑 → ¬ (𝜑 ∧ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 395

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396

This theorem is referenced by: (None)