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Theorem pm5.19 695
Description: Theorem *5.19 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
pm5.19  |-  -.  ( ph 
<->  -.  ph )

Proof of Theorem pm5.19
StepHypRef Expression
1 bi1 117 . . . 4  |-  ( (
ph 
<->  -.  ph )  -> 
( ph  ->  -.  ph ) )
21pm2.01d 607 . . 3  |-  ( (
ph 
<->  -.  ph )  ->  -.  ph )
3 id 19 . . 3  |-  ( (
ph 
<->  -.  ph )  -> 
( ph  <->  -.  ph ) )
42, 3mpbird 166 . 2  |-  ( (
ph 
<->  -.  ph )  ->  ph )
54, 2pm2.65i 628 1  |-  -.  ( ph 
<->  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  pm5.16  813  pclem6  1352  pm5.18im  1363  ru  2908  exmidonfinlem  7054
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