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Mirrors > Home > ILE Home > Th. List > nffvd | Unicode version |
Description: Deduction version of bound-variable hypothesis builder nffv 5479. (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
nffvd.2 | |
nffvd.3 |
Ref | Expression |
---|---|
nffvd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfaba1 2305 | . . 3 | |
2 | nfaba1 2305 | . . 3 | |
3 | 1, 2 | nffv 5479 | . 2 |
4 | nffvd.2 | . . 3 | |
5 | nffvd.3 | . . 3 | |
6 | nfnfc1 2302 | . . . . 5 | |
7 | nfnfc1 2302 | . . . . 5 | |
8 | 6, 7 | nfan 1545 | . . . 4 |
9 | abidnf 2880 | . . . . . 6 | |
10 | 9 | adantr 274 | . . . . 5 |
11 | abidnf 2880 | . . . . . 6 | |
12 | 11 | adantl 275 | . . . . 5 |
13 | 10, 12 | fveq12d 5476 | . . . 4 |
14 | 8, 13 | nfceqdf 2298 | . . 3 |
15 | 4, 5, 14 | syl2anc 409 | . 2 |
16 | 3, 15 | mpbii 147 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1333 wceq 1335 wcel 2128 cab 2143 wnfc 2286 cfv 5171 |
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 3774 df-br 3967 df-iota 5136 df-fv 5179 |
This theorem is referenced by: nfovd 5851 nfixpxy 6663 |
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