Theorem wl-lem-nexmo 33349

Description: This theorem provides a basic working step in proving theorems about E* or E!. (Contributed by Wolf Lammen, 3-Oct-2019.)

Assertion

Ref	Expression
wl-lem-nexmo	|- ( -. E. x ph -> A. x ( ph -> x = z ) )

Proof of Theorem wl-lem-nexmo

Step	Hyp	Ref	Expression
1		alnex 1706	. 2 |- ( A. x -. ph <-> -. E. x ph )
2		pm2.21 120	. . 3 |- ( -. ph -> ( ph -> x = z ) )
3	2	alimi 1739	. 2 |- ( A. x -. ph -> A. x ( ph -> x = z ) )
4	1, 3	sylbir 225	1 |- ( -. E. x ph -> A. x ( ph -> x = z ) )

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

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

This theorem is referenced by: (None)