Theorem nexd 780

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 740	. 2 |- (ph -> A.x -. ps)
4		alnex 716	. 2 |- (A.x -. ps <-> -. E.xps)
5	3, 4	sylib 173	1 |- (ph -> -. E.xps)

Syntax hints:  -. wn 1   -> wi 2  A.wal 672  E.wex 678

This theorem is referenced by:  nexdv 983  axrepnd 3740  axunndlem1 3741  axunnd 3742

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-ex 679

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