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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 5440 | . 2 ⊢ (𝐵 ∈ 𝐶 → (𝐴 × {𝐵}):𝐴⟶𝐶) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐴 × {𝐵}):𝐴⟶𝐶 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 {csn 3614 × cxp 4649 ⟶wf 5238 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4143 ax-pow 4199 ax-pr 4234 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2758 df-un 3153 df-in 3155 df-ss 3162 df-pw 3599 df-sn 3620 df-pr 3621 df-op 3623 df-br 4026 df-opab 4087 df-mpt 4088 df-id 4318 df-xp 4657 df-rel 4658 df-cnv 4659 df-co 4660 df-dm 4661 df-rn 4662 df-fun 5244 df-fn 5245 df-f 5246 |
This theorem is referenced by: 0ct 7152 ctm 7154 infnninfOLD 7170 exmidomni 7187 ofnegsub 8967 0nninf 15418 exmidsbthrlem 15436 |
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