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Theorem fndmdifcom 5519
 Description: The difference set between two functions is commutative. (Contributed by Stefan O'Rear, 17-Jan-2015.)
Assertion
Ref Expression
fndmdifcom

Proof of Theorem fndmdifcom
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 necom 2390 . . . 4
21a1i 9 . . 3
32rabbiia 2666 . 2
4 fndmdif 5518 . 2
5 fndmdif 5518 . . 3
65ancoms 266 . 2
73, 4, 63eqtr4a 2196 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1331   wcel 1480   wne 2306  crab 2418   cdif 3063   cdm 4534   wfn 5113  cfv 5118 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119  ax-sep 4041  ax-pow 4093  ax-pr 4126 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2000  df-mo 2001  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ne 2307  df-ral 2419  df-rex 2420  df-rab 2423  df-v 2683  df-sbc 2905  df-dif 3068  df-un 3070  df-in 3072  df-ss 3079  df-pw 3507  df-sn 3528  df-pr 3529  df-op 3531  df-uni 3732  df-br 3925  df-opab 3985  df-id 4210  df-xp 4540  df-rel 4541  df-cnv 4542  df-co 4543  df-dm 4544  df-iota 5083  df-fun 5120  df-fn 5121  df-fv 5126 This theorem is referenced by: (None)
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