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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 3575 |
. 2
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8 | 7 | mptru 1372 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2170 |
This theorem depends on definitions: df-bi 117 df-tru 1366 df-fal 1369 df-nf 1471 df-sb 1773 df-clab 2175 df-cleq 2181 df-clel 2184 df-nfc 2320 df-if 3549 |
This theorem is referenced by: nfsum1 11381 nfsum 11382 sumrbdclem 11402 summodclem2a 11406 zsumdc 11409 fsum3 11412 isumss 11416 isumss2 11418 fsum3cvg2 11419 nfcprod1 11579 nfcprod 11580 cbvprod 11583 prodrbdclem 11596 prodmodclem2a 11601 zproddc 11604 fprodseq 11608 fprodntrivap 11609 prodssdc 11614 pcmpt 12358 pcmptdvds 12360 |
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