Theorem nexdv 1811

Description: Deduction for generalization rule for negated wff. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
nexdv.1	⊢ (𝜑 → ¬ 𝜓)

Assertion

Ref	Expression
nexdv	⊢ (𝜑 → ¬ ∃𝑥𝜓)

Distinct variable group:   𝜑,𝑥

Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem nexdv

Step	Hyp	Ref	Expression
1		ax-17 1419	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
2		nexdv.1	. 2 ⊢ (𝜑 → ¬ 𝜓)
3	1, 2	nexd 1504	1 ⊢ (𝜑 → ¬ ∃𝑥𝜓)

Syntax hints:  ¬ wn 3   → wi 4  ∃wex 1381

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ie2 1383  ax-17 1419

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249

This theorem is referenced by: (None)