Theorem hbe1 1847

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 1621	. 2 |- ( E. x ph <-> -. A. x -. ph )
2		hbn1 1846	. 2 |- ( -. A. x -. ph -> A. x -. A. x -. ph )
3	1, 2	hbxfrbi 1651	1 |- ( E. x ph -> A. x E. x ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1397   E.wex 1620

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1626  ax-4 1639  ax-10 1845

This theorem depends on definitions:  df-bi 185  df-ex 1621

This theorem is referenced by:  nfe1  1848  hba1  1904  equs5e  1987  axie1  2354  ac6s6  30746  exlimexi  33627  vk15.4j  33631  vk15.4jVD  34061