Theorem intnanrt 43033

Description: Introduction of conjunct inside of a contradiction. Would be used in elfvov1 7461. (Contributed by SN, 18-May-2025.)

Assertion

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

Proof of Theorem intnanrt

Step	Hyp	Ref	Expression
1		simpl 488	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
2	1	con3i 155	1 ⊢ (¬ 𝜑 → ¬ (𝜑 ∧ 𝜓))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by: (None)