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Mirrors > Home > ILE Home > Th. List > nffvmpt1 | GIF version |
Description: Bound-variable hypothesis builder for mapping, special case. (Contributed by Mario Carneiro, 25-Dec-2016.) |
Ref | Expression |
---|---|
nffvmpt1 | ⊢ Ⅎ𝑥((𝑥 ∈ 𝐴 ↦ 𝐵)‘𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfmpt1 4057 | . 2 ⊢ Ⅎ𝑥(𝑥 ∈ 𝐴 ↦ 𝐵) | |
2 | nfcv 2299 | . 2 ⊢ Ⅎ𝑥𝐶 | |
3 | 1, 2 | nffv 5478 | 1 ⊢ Ⅎ𝑥((𝑥 ∈ 𝐴 ↦ 𝐵)‘𝐶) |
Colors of variables: wff set class |
Syntax hints: Ⅎwnfc 2286 ↦ cmpt 4025 ‘cfv 5170 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-v 2714 df-un 3106 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-opab 4026 df-mpt 4027 df-iota 5135 df-fv 5178 |
This theorem is referenced by: fvmptt 5559 fmptco 5633 offval2 6047 ofrfval2 6048 mptelixpg 6679 dom2lem 6717 cc2 7187 fsumf1o 11287 fsum3cvg2 11291 fsumadd 11303 isummulc2 11323 isumshft 11387 fprodf1o 11485 txcnp 12671 cnmpt1t 12685 |
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