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Theorem nannanOLD 1385
Description: Obsolete proof of nannan 1384 as of 7-Mar-2020. (Contributed by Jeff Hoffman, 19-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nannanOLD  |-  ( (
ph  -/\  ( ch  -/\  ps ) )  <->  ( ph  ->  ( ch  /\  ps ) ) )

Proof of Theorem nannanOLD
StepHypRef Expression
1 df-nan 1380 . . 3  |-  ( (
ph  -/\  ( ch  -/\  ps ) )  <->  -.  ( ph  /\  ( ch  -/\  ps ) ) )
2 df-nan 1380 . . . 4  |-  ( ( ch  -/\  ps )  <->  -.  ( ch  /\  ps ) )
32anbi2i 698 . . 3  |-  ( (
ph  /\  ( ch  -/\ 
ps ) )  <->  ( ph  /\ 
-.  ( ch  /\  ps ) ) )
41, 3xchbinx 311 . 2  |-  ( (
ph  -/\  ( ch  -/\  ps ) )  <->  -.  ( ph  /\  -.  ( ch 
/\  ps ) ) )
5 iman 425 . 2  |-  ( (
ph  ->  ( ch  /\  ps ) )  <->  -.  ( ph  /\  -.  ( ch 
/\  ps ) ) )
64, 5bitr4i 255 1  |-  ( (
ph  -/\  ( ch  -/\  ps ) )  <->  ( ph  ->  ( ch  /\  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 187    /\ wa 370    -/\ wnan 1379
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-an 372  df-nan 1380
This theorem is referenced by: (None)
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