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Theorem pred0 24270
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 24239 . 2  |-  Pred ( R ,  (/) ,  X
)  =  ( (/)  i^i  ( `' R " { X } ) )
2 incom 3374 . 2  |-  ( (/)  i^i  ( `' R " { X } ) )  =  ( ( `' R " { X } )  i^i  (/) )
3 in0 3493 . 2  |-  ( ( `' R " { X } )  i^i  (/) )  =  (/)
41, 2, 33eqtri 2320 1  |-  Pred ( R ,  (/) ,  X
)  =  (/)
Colors of variables: wff set class
Syntax hints:    = wceq 1632    i^i cin 3164   (/)c0 3468   {csn 3653   `'ccnv 4704   "cima 4708   Predcpred 24238
This theorem is referenced by:  trpred0  24310
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-dif 3168  df-in 3172  df-nul 3469  df-pred 24239
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