Theorem nexr 2177

Description: Inference associated with the contrapositive of 19.8a 2166. (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 2166	. 2 ⊢ (𝜑 → ∃𝑥𝜑)
3	1, 2	mto 196	1 ⊢ ¬ 𝜑

Syntax hints:  ¬ wn 3  ∃wex 1773

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-12 2163

This theorem depends on definitions:  df-bi 206  df-ex 1774

This theorem is referenced by:  alimp-surprise  48039