Theorem hbe1 1891

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 1660	. 2 |- ( E. x ph <-> -. A. x -. ph )
2		hbn1 1890	. 2 |- ( -. A. x -. ph -> A. x -. A. x -. ph )
3	1, 2	hbxfrbi 1690	1 |- ( E. x ph -> A. x E. x ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1435   E.wex 1659

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-10 1889

This theorem depends on definitions:  df-bi 188  df-ex 1660

This theorem is referenced by:  nfe1  1892  hba1  1953  equs5e  2036  axie1  2401  ac6s6  32109  exlimexi  36508  vk15.4j  36512  vk15.4jVD  36941