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Theorem predidm 5391
 Description: Idempotent law for the predecessor class. (Contributed by Scott Fenton, 29-Mar-2011.)
Assertion
Ref Expression
predidm

Proof of Theorem predidm
StepHypRef Expression
1 df-pred 5369 . 2
2 df-pred 5369 . . . . 5
3 inidm 3650 . . . . . 6
43ineq2i 3640 . . . . 5
52, 4eqtr4i 2436 . . . 4
6 inass 3651 . . . 4
75, 6eqtr4i 2436 . . 3
82ineq1i 3639 . . 3
97, 8eqtr4i 2436 . 2
101, 9eqtr4i 2436 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1407   cin 3415  csn 3974  ccnv 4824  cima 4828  cpred 5368 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382 This theorem depends on definitions:  df-bi 187  df-an 371  df-tru 1410  df-ex 1636  df-nf 1640  df-sb 1766  df-clab 2390  df-cleq 2396  df-clel 2399  df-nfc 2554  df-v 3063  df-in 3423  df-pred 5369 This theorem is referenced by: (None)
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