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Theorem mulpiord 8754
 Description: Positive integer multiplication in terms of ordinal multiplication. (Contributed by NM, 27-Aug-1995.) (New usage is discouraged.)
Assertion
Ref Expression
mulpiord

Proof of Theorem mulpiord
StepHypRef Expression
1 opelxpi 4902 . 2
2 fvres 5737 . . 3
3 df-ov 6076 . . . 4
4 df-mi 8743 . . . . 5
54fveq1i 5721 . . . 4
63, 5eqtri 2455 . . 3
7 df-ov 6076 . . 3
82, 6, 73eqtr4g 2492 . 2
91, 8syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  cop 3809   cxp 4868   cres 4872  cfv 5446  (class class class)co 6073   comu 6714  cnpi 8711   cmi 8713 This theorem is referenced by:  mulidpi  8755  mulclpi  8762  mulcompi  8765  mulasspi  8766  distrpi  8767  mulcanpi  8769  ltmpi  8773 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 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-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-xp 4876  df-res 4882  df-iota 5410  df-fv 5454  df-ov 6076  df-mi 8743
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