Theorem 19.8v 1987

Description: Version of 19.8a 2180 with a disjoint variable condition, requiring fewer axioms. Converse of ax5e 1913. (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 1911	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
2	1	19.8w 1983	1 ⊢ (𝜑 → ∃𝑥𝜑)

Syntax hints:   → wi 4  ∃wex 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970

This theorem depends on definitions:  df-bi 209  df-ex 1781

This theorem is referenced by:  19.9v  1988