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Theorem mulpipq2 9320
 Description: Multiplication of positive fractions in terms of positive integers. (Contributed by Mario Carneiro, 8-May-2013.) (New usage is discouraged.)
Assertion
Ref Expression
mulpipq2

Proof of Theorem mulpipq2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 fveq2 5856 . . . 4
21oveq1d 6296 . . 3
3 fveq2 5856 . . . 4
43oveq1d 6296 . . 3
52, 4opeq12d 4210 . 2
6 fveq2 5856 . . . 4
76oveq2d 6297 . . 3
8 fveq2 5856 . . . 4
98oveq2d 6297 . . 3
107, 9opeq12d 4210 . 2
11 df-mpq 9290 . 2
12 opex 4701 . 2
135, 10, 11, 12ovmpt2 6423 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1383   wcel 1804  cop 4020   cxp 4987  cfv 5578  (class class class)co 6281  c1st 6783  c2nd 6784  cnpi 9225   cmi 9227   cmpq 9230 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-9 1808  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421  ax-sep 4558  ax-nul 4566  ax-pr 4676 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-eu 2272  df-mo 2273  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-ral 2798  df-rex 2799  df-rab 2802  df-v 3097  df-sbc 3314  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021  df-uni 4235  df-br 4438  df-opab 4496  df-id 4785  df-xp 4995  df-rel 4996  df-cnv 4997  df-co 4998  df-dm 4999  df-iota 5541  df-fun 5580  df-fv 5586  df-ov 6284  df-oprab 6285  df-mpt2 6286  df-mpq 9290 This theorem is referenced by:  mulpipq  9321  mulcompq  9333  mulerpqlem  9336  mulassnq  9340  distrnq  9342  ltmnq  9353
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