Theorem nexdh 1589

Description: Deduction for generalization rule for negated wff. (Contributed by NM, 2-Jan-2002.)

Hypotheses

Ref	Expression
nexdh.1	|- (ph -> A.xph)
nexdh.2	|- (ph -> -. ps)

Assertion

Ref	Expression
nexdh	|- (ph -> -. E.xps)

Proof of Theorem nexdh

Step	Hyp	Ref	Expression
1		nexdh.1	. . 3 |- (ph -> A.xph)
2		nexdh.2	. . 3 |- (ph -> -. ps)
3	1, 2	alrimih 1565	. 2 |- (ph -> A.x -. ps)
4		alnex 1543	. 2 |- (A.x -. ps <-> -. E.xps)
5	3, 4	sylib 188	1 |- (ph -> -. E.xps)

This proof depends on syntax axioms:  -. wn 3   -> wi 4  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:  nexd  1771