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Mirrors > Home > ILE Home > Th. List > nfif | Unicode version |
Description: Bound-variable hypothesis builder for a conditional operator. (Contributed by NM, 16-Feb-2005.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
nfif.1 | |
nfif.2 | |
nfif.3 |
Ref | Expression |
---|---|
nfif |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfif.1 | . . . 4 | |
2 | 1 | a1i 9 | . . 3 |
3 | nfif.2 | . . . 4 | |
4 | 3 | a1i 9 | . . 3 |
5 | nfif.3 | . . . 4 | |
6 | 5 | a1i 9 | . . 3 |
7 | 2, 4, 6 | nfifd 3376 | . 2 |
8 | 7 | trud 1293 | 1 |
Colors of variables: wff set class |
Syntax hints: wtru 1285 wnf 1389 wnfc 2206 cif 3351 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-if 3352 |
This theorem is referenced by: nfsum1 10193 nfsum 10194 |
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