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Theorem pred0 24199
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 24168 . 2  |-  Pred ( R ,  (/) ,  X
)  =  ( (/)  i^i  ( `' R " { X } ) )
2 incom 3361 . 2  |-  ( (/)  i^i  ( `' R " { X } ) )  =  ( ( `' R " { X } )  i^i  (/) )
3 in0 3480 . 2  |-  ( ( `' R " { X } )  i^i  (/) )  =  (/)
41, 2, 33eqtri 2307 1  |-  Pred ( R ,  (/) ,  X
)  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1623    i^i cin 3151   (/)c0 3455   {csn 3640   `'ccnv 4688   "cima 4692   Predcpred 24167
This theorem is referenced by:  trpred0  24239
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-dif 3155  df-in 3159  df-nul 3456  df-pred 24168
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