Theorem nrex 1270

Description: Inference adding restricted existential quantifier to negated wff.

Hypothesis

Ref	Expression
nrex.1	|- (x e. A -> -. ps)

Assertion

Ref	Expression
nrex	|- -. E.x e. A ps

Proof of Theorem nrex

Step	Hyp	Ref	Expression
1		nrex.1	. . 3 |- (x e. A -> -. ps)
2	1	rgen 1247	. 2 |- A.x e. A -. ps
3		ralnex 1209	. 2 |- (A.x e. A -. ps <-> -. E.x e. A ps)
4	2, 3	mpbi 164	1 |- -. E.x e. A ps

Syntax hints:  -. wn 1   -> wi 2   e. wcel 1092  A.wral 1201  E.wrex 1202

This theorem is referenced by:  rex0 1717  iun0 2028  orduninsuc 2365  cfsuc 3709  nominpos 4509  ruclem37 4921  hatomistic 5755

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-an 198  df-ex 679  df-ral 1205  df-rex 1206

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