Theorem nexr 1706

Description: Inference from 19.8a 1604. (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 1604	. 2 ⊢ (𝜑 → ∃𝑥𝜑)
3	1, 2	mto 663	1 ⊢ ¬ 𝜑

Syntax hints:  ¬ wn 3  ∃wex 1506

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524

This theorem depends on definitions:  df-bi 117

This theorem is referenced by: (None)