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Theorem nebidc 2279
Description: Contraposition law for inequality. (Contributed by Jim Kingdon, 19-May-2018.)
Assertion
Ref Expression
nebidc DECID DECID  C  D  C  D  =/=  C  =/=  D

Proof of Theorem nebidc
StepHypRef Expression
1 id 19 . . . 4  C  D  C  D
21necon3bid 2240 . . 3  C  D  =/=  C  =/= 
D
3 id 19 . . . . . . . 8  =/=  C  =/= 
D  =/=  C  =/= 
D
43a1d 22 . . . . . . 7  =/=  C  =/= 
D DECID  C  D  =/=  C  =/= 
D
54a1d 22 . . . . . 6  =/=  C  =/= 
D DECID DECID  C  D  =/=  C  =/= 
D
65necon4biddc 2274 . . . . 5  =/=  C  =/= 
D DECID DECID  C  D  C  D
76com3l 75 . . . 4 DECID DECID  C  D  =/=  C  =/=  D  C  D
87imp 115 . . 3 DECID DECID  C  D  =/=  C  =/=  D  C  D
92, 8impbid2 131 . 2 DECID DECID  C  D  C  D  =/=  C  =/=  D
109ex 108 1 DECID DECID  C  D  C  D  =/=  C  =/=  D
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  DECID wdc 741   wceq 1242    =/= wne 2201
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110  df-dc 742  df-ne 2203
This theorem is referenced by: (None)
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