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Theorem ssdif 3179
 Description: Difference law for subsets. (Contributed by NM, 28-May-1998.)
Assertion
Ref Expression
ssdif

Proof of Theorem ssdif
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssel 3059 . . . 4
21anim1d 332 . . 3
3 eldif 3048 . . 3
4 eldif 3048 . . 3
52, 3, 43imtr4g 204 . 2
65ssrdv 3071 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 103   wcel 1463   cdif 3036   wss 3039 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 586  ax-in2 587  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-dif 3041  df-in 3045  df-ss 3052 This theorem is referenced by:  ssdifd  3180  phpm  6725  difinfinf  6952
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