Theorem dfrex2 1212

Description: Relationship between restricted universal and existential quantifiers.

Assertion

Ref	Expression
dfrex2	|- (E.x e. A ph <-> -. A.x e. A -. ph)

Proof of Theorem dfrex2

Step	Hyp	Ref	Expression
1		ralnex 1209	. 2 |- (A.x e. A -. ph <-> -. E.x e. A ph)
2	1	bicon2i 194	1 |- (E.x e. A ph <-> -. A.x e. A -. ph)

Syntax hints:  -. wn 1   <-> wb 127  A.wral 1201  E.wrex 1202

This theorem is referenced by:  r19.35 1298  r19.9rzv 1768  supnub 2162  cbvexfo 2924  tz7.49 2997  abianfp 3000  infxpidmlem12 4944  chpssat 5756  chrelat3t 5762

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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