Theorem nexdOLD 2186

Description: Obsolete proof of nexd 2076 as of 6-Oct-2021. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nexdOLD.1	⊢ Ⅎ𝑥𝜑
nexdOLD.2	⊢ (𝜑 → ¬ 𝜓)

Assertion

Ref	Expression
nexdOLD	⊢ (𝜑 → ¬ ∃𝑥𝜓)

Proof of Theorem nexdOLD

Step	Hyp	Ref	Expression
1		nexdOLD.1	. . 3 ⊢ Ⅎ𝑥𝜑
2	1	nfriOLD 2177	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
3		nexdOLD.2	. 2 ⊢ (𝜑 → ¬ 𝜓)
4	2, 3	nexdh 1779	1 ⊢ (𝜑 → ¬ ∃𝑥𝜓)

Syntax hints:  ¬ wn 3   → wi 4  ∃wex 1695  ℲwnfOLD 1700

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nfOLD 1712

This theorem is referenced by: (None)