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Theorem iscomb 25437
 Description: The predicate "is a commutative operation". (Contributed by FL, 14-Sep-2010.)
Hypothesis
Ref Expression
iscom.1
Assertion
Ref Expression
iscomb

Proof of Theorem iscomb
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 iscom.1 . . . . 5
21iscom 25436 . . . 4
3 oveq1 5881 . . . . . . . 8
4 oveq2 5882 . . . . . . . 8
53, 4eqeq12d 2310 . . . . . . 7
6 oveq2 5882 . . . . . . . 8
7 oveq1 5881 . . . . . . . 8
86, 7eqeq12d 2310 . . . . . . 7
95, 8rspc2v 2903 . . . . . 6
109ex 423 . . . . 5
1110com3r 73 . . . 4
122, 11syl6bi 219 . . 3
1312pm2.43i 43 . 2
14133imp 1145 1
 Colors of variables: wff set class Syntax hints:   wi 4   w3a 934   wceq 1632   wcel 1696  wral 2556   cdm 4705  (class class class)co 5874  ccm1 25434 This theorem is referenced by:  reacomsmgrp1  25446  reacomsmgrp2  25447  reacomsmgrp3  25448  fprodadd  25455 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-dm 4715  df-iota 5235  df-fv 5279  df-ov 5877  df-com1 25435
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