Theorem nexr 1760

Description: Inference from 19.8a 1756. (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 1756	. 2 ⊢ (φ → ∃xφ)
3	1, 2	mto 167	1 ⊢ ¬ φ

Syntax hints:  ¬ wn 3  ∃wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by: (None)