Theorem hbexOLD 2152

Description: Obsolete proof of hbex 2156 as of 16-Oct-2021. (Contributed by NM, 12-Mar-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
hbexOLD.1	|- ( ph -> A. x ph )

Assertion

Ref	Expression
hbexOLD	|- ( E. y ph -> A. x E. y ph )

Proof of Theorem hbexOLD

Step	Hyp	Ref	Expression
1		df-ex 1705	. 2 |- ( E. y ph <-> -. A. y -. ph )
2		hbexOLD.1	. . . . 5 |- ( ph -> A. x ph )
3	2	hbn 2146	. . . 4 |- ( -. ph -> A. x -. ph )
4	3	hbal 2036	. . 3 |- ( A. y -. ph -> A. x A. y -. ph )
5	4	hbn 2146	. 2 |- ( -. A. y -. ph -> A. x -. A. y -. ph )
6	1, 5	hbxfrbi 1752	1 |- ( E. y ph -> A. x E. y ph )

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  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710

This theorem is referenced by:  nfexOLD  2155