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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 3542 | . 2 |
8 | 7 | mptru 1351 | 1 |
Colors of variables: wff set class |
Syntax hints: wtru 1343 wnf 1447 wnfc 2293 cif 3515 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-if 3516 |
This theorem is referenced by: nfsum1 11283 nfsum 11284 sumrbdclem 11304 summodclem2a 11308 zsumdc 11311 fsum3 11314 isumss 11318 isumss2 11320 fsum3cvg2 11321 nfcprod1 11481 nfcprod 11482 cbvprod 11485 prodrbdclem 11498 prodmodclem2a 11503 zproddc 11506 fprodseq 11510 fprodntrivap 11511 prodssdc 11516 pcmpt 12252 pcmptdvds 12254 |
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