Theorem nf3 1657

Description: An alternate definition of df-nf 1449. (Contributed by Mario Carneiro, 24-Sep-2016.)

Assertion

Ref	Expression
nf3	|- ( F/ x ph <-> A. x ( E. x ph -> ph ) )

Proof of Theorem nf3

Step	Hyp	Ref	Expression
1		nf2 1656	. 2 |- ( F/ x ph <-> ( E. x ph -> A. x ph ) )
2		nfe1 1484	. . . 4 |- F/ x E. x ph
3	2	nfri 1507	. . 3 |- ( E. x ph -> A. x E. x ph )
4	3	19.21h 1545	. 2 |- ( A. x ( E. x ph -> ph ) <-> ( E. x ph -> A. x ph ) )
5	1, 4	bitr4i 186	1 |- ( F/ x ph <-> A. x ( E. x ph -> ph ) )

Syntax hints:   -> wi 4   <-> wb 104   A.wal 1341   F/wnf 1448   E.wex 1480

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-ial 1522  ax-i5r 1523

This theorem depends on definitions:  df-bi 116  df-nf 1449

This theorem is referenced by:  hbe1a  2011  eusv2nf  4434