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Mirrors > Home > ILE Home > Th. List > nfiotaw | GIF version |
Description: Bound-variable hypothesis builder for the ℩ class. (Contributed by NM, 23-Aug-2011.) |
Ref | Expression |
---|---|
nfiotaw.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
nfiotaw | ⊢ Ⅎ𝑥(℩𝑦𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1443 | . . 3 ⊢ Ⅎ𝑦⊤ | |
2 | nfiotaw.1 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
3 | 2 | a1i 9 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) |
4 | 1, 3 | nfiotadw 5099 | . 2 ⊢ (⊤ → Ⅎ𝑥(℩𝑦𝜑)) |
5 | 4 | mptru 1341 | 1 ⊢ Ⅎ𝑥(℩𝑦𝜑) |
Colors of variables: wff set class |
Syntax hints: ⊤wtru 1333 Ⅎwnf 1437 Ⅎwnfc 2269 ℩cio 5094 |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rex 2423 df-sn 3538 df-uni 3745 df-iota 5096 |
This theorem is referenced by: csbiotag 5124 nffv 5439 nfsum1 11157 nfsum 11158 nfcprod1 11355 nfcprod 11356 |
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