![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > nfmpt22 | GIF version |
Description: Bound-variable hypothesis builder for an operation in maps-to notation. (Contributed by NM, 27-Aug-2013.) |
Ref | Expression |
---|---|
nfmpt22 | ⊢ Ⅎ𝑦(𝑥 ∈ 𝐴, 𝑦 ∈ 𝐵 ↦ 𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mpt2 5548 | . 2 ⊢ (𝑥 ∈ 𝐴, 𝑦 ∈ 𝐵 ↦ 𝐶) = {〈〈𝑥, 𝑦〉, 𝑧〉 ∣ ((𝑥 ∈ 𝐴 ∧ 𝑦 ∈ 𝐵) ∧ 𝑧 = 𝐶)} | |
2 | nfoprab2 5586 | . 2 ⊢ Ⅎ𝑦{〈〈𝑥, 𝑦〉, 𝑧〉 ∣ ((𝑥 ∈ 𝐴 ∧ 𝑦 ∈ 𝐵) ∧ 𝑧 = 𝐶)} | |
3 | 1, 2 | nfcxfr 2217 | 1 ⊢ Ⅎ𝑦(𝑥 ∈ 𝐴, 𝑦 ∈ 𝐵 ↦ 𝐶) |
Colors of variables: wff set class |
Syntax hints: ∧ wa 102 = wceq 1285 ∈ wcel 1434 Ⅎwnfc 2207 {coprab 5544 ↦ cmpt2 5545 |
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 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2064 |
This theorem depends on definitions: df-bi 115 df-nf 1391 df-sb 1687 df-clab 2069 df-cleq 2075 df-clel 2078 df-nfc 2209 df-oprab 5547 df-mpt2 5548 |
This theorem is referenced by: ovmpt2s 5655 ov2gf 5656 ovmpt2dxf 5657 ovmpt2df 5663 ovmpt2dv2 5665 xpcomco 6370 |
Copyright terms: Public domain | W3C validator |