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Theorem mulpipq 8817
 Description: Multiplication of positive fractions in terms of positive integers. (Contributed by NM, 28-Aug-1995.) (Revised by Mario Carneiro, 8-May-2013.) (New usage is discouraged.)
Assertion
Ref Expression
mulpipq

Proof of Theorem mulpipq
StepHypRef Expression
1 opelxpi 4910 . . 3
2 opelxpi 4910 . . 3
3 mulpipq2 8816 . . 3
41, 2, 3syl2an 464 . 2
5 op1stg 6359 . . . 4
6 op1stg 6359 . . . 4
75, 6oveqan12d 6100 . . 3
8 op2ndg 6360 . . . 4
9 op2ndg 6360 . . . 4
108, 9oveqan12d 6100 . . 3
117, 10opeq12d 3992 . 2
124, 11eqtrd 2468 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  cop 3817   cxp 4876  cfv 5454  (class class class)co 6081  c1st 6347  c2nd 6348  cnpi 8719   cmi 8721   cmpq 8724 This theorem is referenced by:  mulassnq  8836  distrnq  8838  mulidnq  8840  recmulnq  8841 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-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403  ax-un 4701 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-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-iota 5418  df-fun 5456  df-fv 5462  df-ov 6084  df-oprab 6085  df-mpt2 6086  df-1st 6349  df-2nd 6350  df-mpq 8786
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