Theorem nf2 1866

Description: An alternative definition of df-nf 1545, which does not involve nested quantifiers on the same variable. (Contributed by Mario Carneiro, 24-Sep-2016.)

Assertion

Ref	Expression
nf2	|- ( F/xph <-> (E.xph -> A.xph))

Proof of Theorem nf2

Step	Hyp	Ref	Expression
1		df-nf 1545	. 2 |- ( F/xph <-> A.x(ph -> A.xph))
2		nfa1 1788	. . 3 |- F/xA.xph
3	2	19.23 1801	. 2 |- (A.x(ph -> A.xph) <-> (E.xph -> A.xph))
4	1, 3	bitri 240	1 |- ( F/xph <-> (E.xph -> A.xph))

Syntax hints:   -> wi 4   <-> wb 176  A.wal 1540  E.wex 1541   F/wnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by:  nf3  1867  nf4  1868