Theorem nexr 1680

Description: Inference from 19.8a 1578. (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 1578	. 2 ⊢ (𝜑 → ∃𝑥𝜑)
3	1, 2	mto 652	1 ⊢ ¬ 𝜑

Syntax hints:  ¬ wn 3  ∃wex 1480

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)