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Theorem nic-mpALT 1427
Description: A direct proof of nic-mp 1426. (Contributed by NM, 30-Dec-2008.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nic-jmin  |-  ph
nic-jmaj  |-  ( ph  -/\  ( ch  -/\  ps )
)
Assertion
Ref Expression
nic-mpALT  |-  ps

Proof of Theorem nic-mpALT
StepHypRef Expression
1 nic-jmin . 2  |-  ph
2 nic-jmaj . . . . 5  |-  ( ph  -/\  ( ch  -/\  ps )
)
3 df-nan 1288 . . . . . 6  |-  ( (
ph  -/\  ( ch  -/\  ps ) )  <->  -.  ( ph  /\  ( ch  -/\  ps ) ) )
4 df-nan 1288 . . . . . . 7  |-  ( ( ch  -/\  ps )  <->  -.  ( ch  /\  ps ) )
54anbi2i 675 . . . . . 6  |-  ( (
ph  /\  ( ch  -/\ 
ps ) )  <->  ( ph  /\ 
-.  ( ch  /\  ps ) ) )
63, 5xchbinx 301 . . . . 5  |-  ( (
ph  -/\  ( ch  -/\  ps ) )  <->  -.  ( ph  /\  -.  ( ch 
/\  ps ) ) )
72, 6mpbi 199 . . . 4  |-  -.  ( ph  /\  -.  ( ch 
/\  ps ) )
8 iman 413 . . . 4  |-  ( (
ph  ->  ( ch  /\  ps ) )  <->  -.  ( ph  /\  -.  ( ch 
/\  ps ) ) )
97, 8mpbir 200 . . 3  |-  ( ph  ->  ( ch  /\  ps ) )
109simprd 449 . 2  |-  ( ph  ->  ps )
111, 10ax-mp 8 1  |-  ps
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 358    -/\ wnan 1287
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-an 360  df-nan 1288
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