Theorem bj-nexrt 37686

Description: Closed form of nexr 2228. Contrapositive of 19.8a 2217. (Contributed by BJ, 20-Oct-2019.)

Assertion

Ref	Expression
bj-nexrt	⊢ (¬ ∃𝑥𝜑 → ¬ 𝜑)

Proof of Theorem bj-nexrt

Step	Hyp	Ref	Expression
1		19.8a 2217	. 2 ⊢ (𝜑 → ∃𝑥𝜑)
2	1	con3i 155	1 ⊢ (¬ ∃𝑥𝜑 → ¬ 𝜑)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4  ∃wex 1811

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-12 2212

This proof depends on definitions:  df-bi 210  df-ex 1812

This theorem is used by: (None)