Theorem dfral2 1655

Description: Relationship between restricted universal and existential quantifiers.

Assertion

Ref	Expression
dfral2	|- (A.x e. A ph <-> -. E.x e. A -. ph)

Proof of Theorem dfral2

Step	Hyp	Ref	Expression
1		rexnal 1654	. 2 |- (E.x e. A -. ph <-> -. A.x e. A ph)
2	1	con2bii 221	1 |- (A.x e. A ph <-> -. E.x e. A -. ph)

Syntax hints:  -. wn 2   <-> wb 146  A.wral 1645  E.wrex 1646

This theorem is referenced by:  ac6n 4757  indstr 6461  lnopcon 9963  lnfncon 9990  str 10184  hstr 10192

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-an 225  df-ex 981  df-ral 1649  df-rex 1650

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