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Theorem isla 14667
 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 5072 . . . 4
2 isla.1 . . . 4
31, 2syl6eqr 2488 . . 3
4 oveq1 6090 . . . . . 6
54, 3eleq12d 2506 . . . . 5
6 oveq1 6090 . . . . . 6
76, 3eleq12d 2506 . . . . 5
85, 7anbi12d 693 . . . 4
93, 8raleqbidv 2918 . . 3
103, 9raleqbidv 2918 . 2
11 df-lar 14635 . 2
1210, 11elrab2 3096 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   wceq 1653   wcel 1726  wral 2707  cpr 3817   cdm 4880  (class class class)co 6083  cps 14626   cspw 14628   cinf 14629  cla 14630 This theorem is referenced by:  laspwcl  14668  lanfwcl  14669  laps  14670 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-dm 4890  df-iota 5420  df-fv 5464  df-ov 6086  df-lar 14635
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