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Mirrors > Home > ILE Home > Th. List > fconst6 | GIF version |
Description: A constant function as a mapping. (Contributed by Jeff Madsen, 30-Nov-2009.) (Revised by Mario Carneiro, 22-Apr-2015.) |
Ref | Expression |
---|---|
fconst6.1 | ⊢ 𝐵 ∈ 𝐶 |
Ref | Expression |
---|---|
fconst6 | ⊢ (𝐴 × {𝐵}):𝐴⟶𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fconst6.1 | . 2 ⊢ 𝐵 ∈ 𝐶 | |
2 | fconst6g 5209 | . 2 ⊢ (𝐵 ∈ 𝐶 → (𝐴 × {𝐵}):𝐴⟶𝐶) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ (𝐴 × {𝐵}):𝐴⟶𝐶 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1438 {csn 3446 × cxp 4436 ⟶wf 5011 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3957 ax-pow 4009 ax-pr 4036 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-rex 2365 df-v 2621 df-un 3003 df-in 3005 df-ss 3012 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-br 3846 df-opab 3900 df-mpt 3901 df-id 4120 df-xp 4444 df-rel 4445 df-cnv 4446 df-co 4447 df-dm 4448 df-rn 4449 df-fun 5017 df-fn 5018 df-f 5019 |
This theorem is referenced by: exmidomni 6798 infnninf 6805 0nninf 11893 exmidsbthrlem 11912 |
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