Theorem 19.8v 2016

Description: Version of 19.8a 2220 with a disjoint variable condition, requiring fewer axioms. Converse of ax5e 1945. (Contributed by BJ, 12-Mar-2020.)

Assertion

Ref	Expression
19.8v	⊢ (𝜑 → ∃𝑥𝜑)

Distinct variable group:   𝜑,𝑥

Proof of Theorem 19.8v

Step	Hyp	Ref	Expression
1		ax-5 1943	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
2	1	19.8w 2011	1 ⊢ (𝜑 → ∃𝑥𝜑)

This proof depends on syntax axioms:   → wi 4  ∃wex 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000

This proof depends on definitions:  df-bi 210  df-ex 1813

This theorem is used by:  19.9v  2017