Theorem axc7e 2133

Description: Abbreviated version of axc7 2132 using the existential quantifier. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
axc7e	|- ( E. x A. x ph -> ph )

Proof of Theorem axc7e

Step	Hyp	Ref	Expression
1		hbe1a 2022	. 2 |- ( E. x A. x ph -> A. x ph )
2		sp 2053	. 2 |- ( A. x ph -> ph )
3	1, 2	syl 17	1 |- ( E. x A. x ph -> ph )

Syntax hints:   -> 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-12 2047

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

This theorem is referenced by:  19.9ht  2143  bj-axc10  32707