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Theorem pm5.19 655
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 116 . . . 4  |-  ( (
ph 
<->  -.  ph )  -> 
( ph  ->  -.  ph ) )
21pm2.01d 581 . . 3  |-  ( (
ph 
<->  -.  ph )  ->  -.  ph )
3 id 19 . . 3  |-  ( (
ph 
<->  -.  ph )  -> 
( ph  <->  -.  ph ) )
42, 3mpbird 165 . 2  |-  ( (
ph 
<->  -.  ph )  ->  ph )
54, 2pm2.65i 601 1  |-  -.  ( ph 
<->  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  pm5.16  771  pclem6  1306  pm5.18im  1317  ru  2815
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