Theorem 2nalexn 1573

Description: Part of theorem *11.5 in [WhiteheadRussell] p. 164. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

Ref	Expression
2nalexn	|- (-. A.xA.yph <-> E.xE.y -. ph)

Proof of Theorem 2nalexn

Step	Hyp	Ref	Expression
1		df-ex 1542	. . 3 |- (E.xE.y -. ph <-> -. A.x -. E.y -. ph)
2		alex 1572	. . . 4 |- (A.yph <-> -. E.y -. ph)
3	2	albii 1566	. . 3 |- (A.xA.yph <-> A.x -. E.y -. ph)
4	1, 3	xchbinxr 302	. 2 |- (E.xE.y -. ph <-> -. A.xA.yph)
5	4	bicomi 193	1 |- (-. A.xA.yph <-> E.xE.y -. ph)

This proof depends on syntax axioms:  -. wn 3   <-> wb 176  A.wal 1540  E.wex 1541

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This proof depends on definitions:  df-bi 177  df-ex 1542

This theorem is used by:  spc2gv  2943