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Theorem predeq1 25352
 Description: Equality theorem for the predecessor class. (Contributed by Scott Fenton, 2-Feb-2011.)
Assertion
Ref Expression
predeq1

Proof of Theorem predeq1
StepHypRef Expression
1 cnveq 5000 . . . 4
21imaeq1d 5156 . . 3
32ineq2d 3499 . 2
4 df-pred 25351 . 2
5 df-pred 25351 . 2
63, 4, 53eqtr4g 2458 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1649   cin 3276  csn 3771  ccnv 4831  cima 4835  cpred 25350 This theorem is referenced by:  trpredeq1  25406 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2382 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2526  df-rab 2672  df-v 2915  df-dif 3280  df-un 3282  df-in 3284  df-ss 3291  df-nul 3586  df-if 3697  df-sn 3777  df-pr 3778  df-op 3780  df-br 4168  df-opab 4222  df-cnv 4840  df-dm 4842  df-rn 4843  df-res 4844  df-ima 4845  df-pred 25351
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