Theorem nexd 1102

Description: Deduction for generalization rule for negated wff.

Hypotheses

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

Assertion

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

Proof of Theorem nexd

Step	Hyp	Ref	Expression
1		nexd.1	. . 3 |- (ph -> A.xph)
2		nexd.2	. . 3 |- (ph -> -. ps)
3	1, 2	19.21ai 998	. 2 |- (ph -> A.x -. ps)
4		alnex 1033	. 2 |- (A.x -. ps <-> -. E.xps)
5	3, 4	sylib 198	1 |- (ph -> -. E.xps)

Syntax hints:  -. wn 2   -> wi 3  A.wal 954  E.wex 980

This theorem is referenced by:  nexdv 1326  axrepnd 4946  axunndlem1 4947  axunnd 4948

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975

This theorem depends on definitions:  df-bi 147  df-ex 981

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