Theorem nexr 2231

Description: Inference associated with the contrapositive of 19.8a 2220. (Contributed by Jeff Hankins, 26-Jul-2009.)

Hypothesis

Ref	Expression
nexr.1	⊢ ¬ ∃𝑥𝜑

Assertion

Ref	Expression
nexr	⊢ ¬ 𝜑

Proof of Theorem nexr

Step	Hyp	Ref	Expression
1		nexr.1	. 2 ⊢ ¬ ∃𝑥𝜑
2		19.8a 2220	. 2 ⊢ (𝜑 → ∃𝑥𝜑)
3	1, 2	mto 200	1 ⊢ ¬ 𝜑

This proof depends on syntax axioms:  ¬ wn 3  ∃wex 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-12 2216

This proof depends on definitions:  df-bi 210  df-ex 1813

This theorem is used by:  alimp-surprise  50591