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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 8817 | . 2 ⊢ ↑m = (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑓 ∣ 𝑓:𝑦⟶𝑥}) | |
2 | 1 | reldmmpo 7537 | 1 ⊢ Rel dom ↑m |
Colors of variables: wff setvar class |
Syntax hints: {cab 2710 Vcvv 3475 dom cdm 5674 Rel wrel 5679 ⟶wf 6535 ↑m cmap 8815 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-sep 5297 ax-nul 5304 ax-pr 5425 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-rab 3434 df-v 3477 df-dif 3949 df-un 3951 df-in 3953 df-ss 3963 df-nul 4321 df-if 4527 df-sn 4627 df-pr 4629 df-op 4633 df-br 5147 df-opab 5209 df-xp 5680 df-rel 5681 df-dm 5684 df-oprab 7407 df-mpo 7408 df-map 8817 |
This theorem is referenced by: mapssfset 8840 mapdom2 9143 efmndbas 18747 smatrcl 32713 mapco2g 41384 naryfvalixp 47216 1aryenef 47232 2aryenef 47243 |
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