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Theorem sloteq 12001
 Description: Equality theorem for the Slot construction. The converse holds if (or ) is a set. (Contributed by BJ, 27-Dec-2021.)
Assertion
Ref Expression
sloteq Slot Slot

Proof of Theorem sloteq
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fveq2 5428 . . 3
21mpteq2dv 4026 . 2
3 df-slot 12000 . 2 Slot
4 df-slot 12000 . 2 Slot
52, 3, 43eqtr4g 2198 1 Slot Slot
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1332  cvv 2689   cmpt 3996  cfv 5130  Slot cslot 11995 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-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2691  df-un 3079  df-sn 3537  df-pr 3538  df-op 3540  df-uni 3744  df-br 3937  df-opab 3997  df-mpt 3998  df-iota 5095  df-fv 5138  df-slot 12000 This theorem is referenced by:  ndxid  12020
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