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Theorem pred0 25474
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 25439 . 2  |-  Pred ( R ,  (/) ,  X
)  =  ( (/)  i^i  ( `' R " { X } ) )
2 incom 3533 . 2  |-  ( (/)  i^i  ( `' R " { X } ) )  =  ( ( `' R " { X } )  i^i  (/) )
3 in0 3653 . 2  |-  ( ( `' R " { X } )  i^i  (/) )  =  (/)
41, 2, 33eqtri 2460 1  |-  Pred ( R ,  (/) ,  X
)  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1652    i^i cin 3319   (/)c0 3628   {csn 3814   `'ccnv 4877   "cima 4881   Predcpred 25438
This theorem is referenced by:  trpred0  25514
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-dif 3323  df-in 3327  df-nul 3629  df-pred 25439
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