Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  mul4i Structured version   Unicode version

Theorem mul4i 9263
 Description: Rearrangement of 4 factors. (Contributed by NM, 16-Feb-1995.)
Hypotheses
Ref Expression
mul.1
mul.2
mul.3
mul4.4
Assertion
Ref Expression
mul4i

Proof of Theorem mul4i
StepHypRef Expression
1 mul.1 . 2
2 mul.2 . 2
3 mul.3 . 2
4 mul4.4 . 2
5 mul4 9235 . 2
61, 2, 3, 4, 5mp4an 655 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   wcel 1725  (class class class)co 6081  cc 8988   cmul 8995 This theorem is referenced by:  faclbnd4lem1  11584  bposlem8  21075  normlem1  22612 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-mulcl 9052  ax-mulcom 9054  ax-mulass 9056 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2711  df-rab 2714  df-v 2958  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-iota 5418  df-fv 5462  df-ov 6084
 Copyright terms: Public domain W3C validator