Theorem nf5 2116

Description: Alternate definition of df-nf 1710. (Contributed by Mario Carneiro, 11-Aug-2016.) df-nf 1710 changed. (Revised by Wolf Lammen, 11-Sep-2021.)

Assertion

Ref	Expression
nf5	|- ( F/ x ph <-> A. x ( ph -> A. x ph ) )

Proof of Theorem nf5

Step	Hyp	Ref	Expression
1		df-nf 1710	. 2 |- ( F/ x ph <-> ( E. x ph -> A. x ph ) )
2		nfa1 2028	. . 3 |- F/ x A. x ph
3	2	19.23 2080	. 2 |- ( A. x ( ph -> A. x ph ) <-> ( E. x ph -> A. x ph ) )
4	1, 3	bitr4i 267	1 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   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-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-ex 1705  df-nf 1710

This theorem is referenced by:  nfnf1OLD  2159  drnf1  2329  axie2  2597  xfree  29303  bj-nfdt0  32685  bj-nfalt  32702  bj-nfext  32703  bj-nfs1t  32714  bj-drnf1v  32750  bj-sbnf  32828  wl-sbnf1  33336  hbexg  38772