Theorem 19.9ht 2143

Description: A closed version of 19.9 2072. (Contributed by NM, 13-May-1993.) (Proof shortened by Wolf Lammen, 3-Mar-2018.)

Assertion

Ref	Expression
19.9ht	|- ( A. x ( ph -> A. x ph ) -> ( E. x ph -> ph ) )

Proof of Theorem 19.9ht

Step	Hyp	Ref	Expression
1		exim 1761	. 2 |- ( A. x ( ph -> A. x ph ) -> ( E. x ph -> E. x A. x ph ) )
2		axc7e 2133	. 2 |- ( E. x A. x ph -> ph )
3	1, 2	syl6 35	1 |- ( A. x ( ph -> A. x ph ) -> ( E. 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:  hbntOLD  2145  19.9dOLD  2203  bj-19.9htbi  32694