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Theorem nic-mpALT 1551
 Description: A direct proof of nic-mp 1550. (Contributed by NM, 30-Dec-2008.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nic-jmin
nic-jmaj
Assertion
Ref Expression
nic-mpALT

Proof of Theorem nic-mpALT
StepHypRef Expression
1 nic-jmin . 2
2 nic-jmaj . . . . 5
3 df-nan 1380 . . . . . 6
4 df-nan 1380 . . . . . . 7
54anbi2i 698 . . . . . 6
63, 5xchbinx 311 . . . . 5
72, 6mpbi 211 . . . 4
8 iman 425 . . . 4
97, 8mpbir 212 . . 3
109simprd 464 . 2
111, 10ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   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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