Theorem 19.8v 1981

Description: Version of 19.8a 2180 with a disjoint variable condition, requiring fewer axioms. Converse of ax5e 1911. (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 1909	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
2	1	19.8w 1977	1 ⊢ (𝜑 → ∃𝑥𝜑)

Syntax hints:   → wi 4  ∃wex 1778

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966

This theorem depends on definitions:  df-bi 207  df-ex 1779

This theorem is referenced by:  19.9v  1982