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Mirrors > Home > ILE Home > Th. List > nffvd | Unicode version |
Description: Deduction version of bound-variable hypothesis builder nffv 5506. (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 2318 | . . 3 | |
2 | nfaba1 2318 | . . 3 | |
3 | 1, 2 | nffv 5506 | . 2 |
4 | nffvd.2 | . . 3 | |
5 | nffvd.3 | . . 3 | |
6 | nfnfc1 2315 | . . . . 5 | |
7 | nfnfc1 2315 | . . . . 5 | |
8 | 6, 7 | nfan 1558 | . . . 4 |
9 | abidnf 2898 | . . . . . 6 | |
10 | 9 | adantr 274 | . . . . 5 |
11 | abidnf 2898 | . . . . . 6 | |
12 | 11 | adantl 275 | . . . . 5 |
13 | 10, 12 | fveq12d 5503 | . . . 4 |
14 | 8, 13 | nfceqdf 2311 | . . 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 1346 wceq 1348 wcel 2141 cab 2156 wnfc 2299 cfv 5198 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rex 2454 df-v 2732 df-un 3125 df-sn 3589 df-pr 3590 df-op 3592 df-uni 3797 df-br 3990 df-iota 5160 df-fv 5206 |
This theorem is referenced by: nfovd 5882 nfixpxy 6695 |
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