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Theorem notev 25093
Description: It's false that  ph eventually holds iff  -.  ph always holds. (Contributed by FL, 20-Mar-2011.)
Assertion
Ref Expression
notev  |-  ( -.  <> ph 
<->  [.]  -.  ph )

Proof of Theorem notev
StepHypRef Expression
1 df-dia 25083 . . 3  |-  ( <> ph  <->  -. 
[.]  -.  ph )
21bicomi 193 . 2  |-  ( -. 
[.]  -.  ph  <->  <> ph )
32con1bii 321 1  |-  ( -.  <> ph 
<->  [.]  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176   [.]wbox 25073   <>wdia 25074
This theorem is referenced by:  evpexun  25101  evevifev  25117
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-dia 25083
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