Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  mulpipq2 Unicode version

Theorem mulpipq2 9338
 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 5871 . . . 4
21oveq1d 6311 . . 3
3 fveq2 5871 . . . 4
43oveq1d 6311 . . 3
52, 4opeq12d 4225 . 2
6 fveq2 5871 . . . 4
76oveq2d 6312 . . 3
8 fveq2 5871 . . . 4
98oveq2d 6312 . . 3
107, 9opeq12d 4225 . 2
11 df-mpq 9308 . 2
12 opex 4716 . 2
135, 10, 11, 12ovmpt2 6438 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  <.cop 4035  X.cxp 5002  `cfv 5593  (class class class)co 6296   c1st 6798   c2nd 6799   cnpi 9243   cmi 9245   cmpq 9248 This theorem is referenced by:  mulpipq  9339  mulcompq  9351  mulerpqlem  9354  mulassnq  9358  distrnq  9360  ltmnq  9371 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-iota 5556  df-fun 5595  df-fv 5601  df-ov 6299  df-oprab 6300  df-mpt2 6301  df-mpq 9308
 Copyright terms: Public domain W3C validator