Theorem spvw 1885

Description: Version of sp 2041 when 𝑥 does not occur in 𝜑. Converse of ax-5 1827. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 10-Apr-2017.) (Proof shortened by Wolf Lammen, 4-Dec-2017.)

Assertion

Ref	Expression
spvw	⊢ (∀𝑥𝜑 → 𝜑)

Distinct variable group:   𝜑,𝑥

Proof of Theorem spvw

Step	Hyp	Ref	Expression
1		19.3v 1884	. 2 ⊢ (∀𝑥𝜑 ↔ 𝜑)
2	1	biimpi 205	1 ⊢ (∀𝑥𝜑 → 𝜑)

Syntax hints:   → wi 4  ∀wal 1473

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875

This theorem depends on definitions:  df-bi 196  df-ex 1696

This theorem is referenced by: (None)