Theorem spvw 1824

Description: Version of sp 1947 when x does not occur in ph. Converse of ax-5 1768. 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	|- ( A. x ph -> ph )

Distinct variable group:   ph, x

Proof of Theorem spvw

Step	Hyp	Ref	Expression
1		19.3v 1823	. 2 |- ( A. x ph <-> ph )
2	1	biimpi 199	1 |- ( A. x ph -> ph )

Syntax hints:   -> wi 4   A.wal 1452

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815

This theorem depends on definitions:  df-bi 190  df-ex 1674

This theorem is referenced by: (None)