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Mirrors > Home > ILE Home > Th. List > reldmmap | GIF version |
Description: Set exponentiation is a well-behaved binary operator. (Contributed by Stefan O'Rear, 27-Feb-2015.) |
Ref | Expression |
---|---|
reldmmap | ⊢ Rel dom ↑𝑚 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-map 6552 | . 2 ⊢ ↑𝑚 = (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑓 ∣ 𝑓:𝑦⟶𝑥}) | |
2 | 1 | reldmmpo 5890 | 1 ⊢ Rel dom ↑𝑚 |
Colors of variables: wff set class |
Syntax hints: {cab 2126 Vcvv 2689 dom cdm 4547 Rel wrel 4552 ⟶wf 5127 ↑𝑚 cmap 6550 |
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-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-br 3938 df-opab 3998 df-xp 4553 df-rel 4554 df-dm 4557 df-oprab 5786 df-mpo 5787 df-map 6552 |
This theorem is referenced by: (None) |
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