Theorem nexdvOLD 1865

Description: Obsolete proof of nexdv 1864 as of 10-Oct-2021. (Contributed by NM, 5-Aug-1993.) Reduce dependencies on axioms. (Revised by Wolf Lammen, 13-Jul-2020.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nexdv.1	|- ( ph -> -. ps )

Assertion

Ref	Expression
nexdvOLD	|- ( ph -> -. E. x ps )

Distinct variable group:   ph, x

Allowed substitution hint:   ps( x)

Proof of Theorem nexdvOLD

Step	Hyp	Ref	Expression
1		nexdv.1	. . 3 |- ( ph -> -. ps )
2	1	alrimiv 1855	. 2 |- ( ph -> A. x -. ps )
3		alnex 1706	. 2 |- ( A. x -. ps <-> -. E. x ps )
4	2, 3	sylib 208	1 |- ( ph -> -. E. x ps )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by: (None)