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Mirrors > Home > ILE Home > Th. List > nfmpt1 | GIF version |
Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by FL, 17-Feb-2008.) |
Ref | Expression |
---|---|
nfmpt1 | ⊢ Ⅎ𝑥(𝑥 ∈ 𝐴 ↦ 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mpt 4039 | . 2 ⊢ (𝑥 ∈ 𝐴 ↦ 𝐵) = {〈𝑥, 𝑧〉 ∣ (𝑥 ∈ 𝐴 ∧ 𝑧 = 𝐵)} | |
2 | nfopab1 4045 | . 2 ⊢ Ⅎ𝑥{〈𝑥, 𝑧〉 ∣ (𝑥 ∈ 𝐴 ∧ 𝑧 = 𝐵)} | |
3 | 1, 2 | nfcxfr 2303 | 1 ⊢ Ⅎ𝑥(𝑥 ∈ 𝐴 ↦ 𝐵) |
Colors of variables: wff set class |
Syntax hints: ∧ wa 103 = wceq 1342 ∈ wcel 2135 Ⅎwnfc 2293 {copab 4036 ↦ cmpt 4037 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-opab 4038 df-mpt 4039 |
This theorem is referenced by: nffvmpt1 5491 fvmptss2 5555 fvmptssdm 5564 fvmptdf 5567 mpteqb 5570 fvmptf 5572 ralrnmpt 5621 rexrnmpt 5622 f1ompt 5630 f1mpt 5733 fliftfun 5758 dom2lem 6729 mapxpen 6805 mkvprop 7113 cc3 7200 nfcprod1 11481 cnmpt11 12824 |
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