Theorem nexr 2227

Description: Inference associated with the contrapositive of 19.8a 2216. (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 2216	. 2 ⊢ (𝜑 → ∃𝑥𝜑)
3	1, 2	mto 200	1 ⊢ ¬ 𝜑

This proof depends on syntax axioms:  ¬ wn 3  ∃wex 1808

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-12 2212

This proof depends on definitions:  df-bi 210  df-ex 1809

This theorem is used by:  alimp-surprise  50586