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Theorem isla 14358
 Description: The predicate "is a lattice" i.e. a poset in which any two elements have upper and lower bounds. (Contributed by NM, 12-Jun-2008.)
Hypothesis
Ref Expression
isla.1
Assertion
Ref Expression
isla
Distinct variable groups:   ,,   ,,

Proof of Theorem isla
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dmeq 4895 . . . 4
2 isla.1 . . . 4
31, 2syl6eqr 2346 . . 3
4 oveq1 5881 . . . . . 6
54, 3eleq12d 2364 . . . . 5
6 oveq1 5881 . . . . . 6
76, 3eleq12d 2364 . . . . 5
85, 7anbi12d 691 . . . 4
93, 8raleqbidv 2761 . . 3
103, 9raleqbidv 2761 . 2
11 df-lar 14326 . 2
1210, 11elrab2 2938 1
 Colors of variables: wff set class Syntax hints:   wb 176   wa 358   wceq 1632   wcel 1696  wral 2556  cpr 3654   cdm 4705  (class class class)co 5874  cps 14317   cspw 14319   cinf 14320  cla 14321 This theorem is referenced by:  laspwcl  14359  lanfwcl  14360  laps  14361  tolat  25389  toplat  25393  latdir  25398 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-lar 14326
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