Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  smodm2 Structured version   Unicode version

Theorem smodm2 6609
 Description: The domain of a strictly monotone ordinal function is an ordinal. (Contributed by Mario Carneiro, 12-Mar-2013.)
Assertion
Ref Expression
smodm2

Proof of Theorem smodm2
StepHypRef Expression
1 smodm 6605 . 2
2 fndm 5536 . . . 4
3 ordeq 4580 . . . 4
42, 3syl 16 . . 3
54biimpa 471 . 2
61, 5sylan2 461 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   word 4572   cdm 4870   wfn 5441   wsmo 6599 This theorem is referenced by:  smo11  6618  smoord  6619  smoword  6620  smogt  6621  smorndom  6622  coftr  8145 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 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-in 3319  df-ss 3326  df-uni 4008  df-tr 4295  df-po 4495  df-so 4496  df-fr 4533  df-we 4535  df-ord 4576  df-fn 5449  df-smo 6600
 Copyright terms: Public domain W3C validator