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.

Step	Hyp	Ref	Expression
1		fveq2 5871	. . . 4
2	1	oveq1d 6311	. . 3
3		fveq2 5871	. . . 4
4	3	oveq1d 6311	. . 3
5	2, 4	opeq12d 4225	. 2
6		fveq2 5871	. . . 4
7	6	oveq2d 6312	. . 3
8		fveq2 5871	. . . 4
9	8	oveq2d 6312	. . 3
10	7, 9	opeq12d 4225	. 2
11		df-mpq 9308	. 2
12		opex 4716	. 2
13	5, 10, 11, 12	ovmpt2 6438	1

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