Theorem hbe1 1779

Description: x is not free in E. x ph. (Contributed by NM, 24-Jan-1993.)

Assertion

Ref	Expression
hbe1	|- ( E. x ph -> A. x E. x ph )

Proof of Theorem hbe1

Step	Hyp	Ref	Expression
1		df-ex 1588	. 2 |- ( E. x ph <-> -. A. x -. ph )
2		hbn1 1778	. 2 |- ( -. A. x -. ph -> A. x -. A. x -. ph )
3	1, 2	hbxfrbi 1614	1 |- ( E. x ph -> A. x E. x ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1368   E.wex 1587

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-10 1777

This theorem depends on definitions:  df-bi 185  df-ex 1588

This theorem is referenced by:  nfe1  1780  hba1  1835  equs5e  1919  axie1  2426  ac6s6  29133  exlimexi  31562  vk15.4j  31566  vk15.4jVD  31983