Theorem 19.9t 2071

Description: A closed version of 19.9 2072. (Contributed by NM, 13-May-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.) (Proof shortened by Wolf Lammen, 14-Jul-2020.)

Assertion

Ref	Expression
19.9t	|- ( F/ x ph -> ( E. x ph <-> ph ) )

Proof of Theorem 19.9t

Step	Hyp	Ref	Expression
1		id 22	. . 3 |- ( F/ x ph -> F/ x ph )
2	1	19.9d 2070	. 2 |- ( F/ x ph -> ( E. x ph -> ph ) )
3		19.8a 2052	. 2 |- ( ph -> E. x ph )
4	2, 3	impbid1 215	1 |- ( F/ x ph -> ( E. x ph <-> ph ) )

Syntax hints:   -> wi 4   <-> wb 196   E.wex 1704   F/wnf 1708

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-12 2047

This theorem depends on definitions:  df-bi 197  df-ex 1705  df-nf 1710

This theorem is referenced by:  19.9  2072  19.21t  2073  19.21tOLDOLD  2074  spimt  2253  sbft  2379  vtoclegft  3280  bj-cbv3tb  32711  bj-spimtv  32718  bj-sbftv  32763  bj-equsal1t  32809  bj-19.21t  32817  19.9alt  34252