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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 |
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nfif.2 |
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nfif.3 |
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Ref | Expression |
---|---|
nfif |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfif.1 |
. . . 4
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2 | 1 | a1i 9 |
. . 3
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3 | nfif.2 |
. . . 4
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4 | 3 | a1i 9 |
. . 3
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5 | nfif.3 |
. . . 4
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6 | 5 | a1i 9 |
. . 3
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7 | 2, 4, 6 | nfifd 3446 |
. 2
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8 | 7 | mptru 1308 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 584 ax-in2 585 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 |
This theorem depends on definitions: df-bi 116 df-tru 1302 df-fal 1305 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-if 3422 |
This theorem is referenced by: nfsum1 10964 nfsum 10965 sumrbdclem 10984 summodclem2a 10989 zsumdc 10992 fsum3 10995 isumss 10999 isumss2 11001 fsum3cvg2 11002 |
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