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Theorem caov4 6506
 Description: Rearrange arguments in a commutative, associative operation. (Contributed by NM, 26-Aug-1995.)
Hypotheses
Ref Expression
caov.1
caov.2
caov.3
caov.com
caov.ass
caov.4
Assertion
Ref Expression
caov4
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caov4
StepHypRef Expression
1 caov.2 . . . 4
2 caov.3 . . . 4
3 caov.4 . . . 4
4 caov.com . . . 4
5 caov.ass . . . 4
61, 2, 3, 4, 5caov12 6503 . . 3
76oveq2i 6307 . 2
8 caov.1 . . 3
9 ovex 6324 . . 3
108, 1, 9, 5caovass 6475 . 2
11 ovex 6324 . . 3
128, 2, 11, 5caovass 6475 . 2
137, 10, 123eqtr4i 2496 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395  e.wcel 1818   cvv 3109  (class class class)co 6296 This theorem is referenced by:  caov42  6508  ecopovtrn  7433  adderpqlem  9353  mulerpqlem  9354  ltmnq  9371  reclem3pr  9448  mulcmpblnrlem  9468  distrsr  9489  ltasr  9498  mulgt0sr  9503  axdistr  9556 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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-nul 4581 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-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-iota 5556  df-fv 5601  df-ov 6299
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