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Theorem labs2 25190
 Description: Absorption law. . (Contributed by FL, 12-Dec-2009.)
Hypothesis
Ref Expression
jop1
Assertion
Ref Expression
labs2
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)

Proof of Theorem labs2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 jop1 . . . 4
21islatalg 25183 . . 3
3 simp32 992 . . . . . 6
43ralimi 2618 . . . . 5
54ralimi 2618 . . . 4
653ad2ant3 978 . . 3
72, 6syl6bi 219 . 2
873impia 1148 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   w3a 934   wceq 1623   wcel 1684  wral 2543  cop 3643   cxp 4687   cdm 4689  wf 5251  (class class class)co 5858  clatalg 25181 This theorem is referenced by:  labss2  25191 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214  ax-un 4512 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-rn 4700  df-iota 5219  df-fun 5257  df-fn 5258  df-f 5259  df-fv 5263  df-ov 5861  df-latalg 25182
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