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Theorem pred0 29132
Description: The predecessor class over  (/) is always  (/) (Contributed by Scott Fenton, 16-Apr-2011.)
Assertion
Ref Expression
pred0  |-  Pred ( R ,  (/) ,  X
)  =  (/)

Proof of Theorem pred0
StepHypRef Expression
1 df-pred 29097 . 2  |-  Pred ( R ,  (/) ,  X
)  =  ( (/)  i^i  ( `' R " { X } ) )
2 incom 3691 . 2  |-  ( (/)  i^i  ( `' R " { X } ) )  =  ( ( `' R " { X } )  i^i  (/) )
3 in0 3811 . 2  |-  ( ( `' R " { X } )  i^i  (/) )  =  (/)
41, 2, 33eqtri 2500 1  |-  Pred ( R ,  (/) ,  X
)  =  (/)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1379    i^i cin 3475   (/)c0 3785   {csn 4027   `'ccnv 4998   "cima 5002   Predcpred 29096
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-dif 3479  df-in 3483  df-nul 3786  df-pred 29097
This theorem is referenced by:  trpred0  29172
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