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Mirrors > Home > MPE Home > Th. List > reldmmap | Structured version Visualization version 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 7746 | . 2 ⊢ ↑𝑚 = (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑓 ∣ 𝑓:𝑦⟶𝑥}) | |
2 | 1 | reldmmpt2 6669 | 1 ⊢ Rel dom ↑𝑚 |
Colors of variables: wff setvar class |
Syntax hints: {cab 2596 Vcvv 3173 dom cdm 5038 Rel wrel 5043 ⟶wf 5800 ↑𝑚 cmap 7744 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-9 1986 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-sep 4709 ax-nul 4717 ax-pr 4833 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-3an 1033 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-eu 2462 df-mo 2463 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-rab 2905 df-v 3175 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-if 4037 df-sn 4126 df-pr 4128 df-op 4132 df-br 4584 df-opab 4644 df-xp 5044 df-rel 5045 df-dm 5048 df-oprab 6553 df-mpt2 6554 df-map 7746 |
This theorem is referenced by: mapdom2 8016 smatrcl 29190 mapco2g 36295 |
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