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Mirrors > Home > ILE Home > Th. List > nfinf | Unicode version |
Description: Hypothesis builder for infimum. (Contributed by AV, 2-Sep-2020.) |
Ref | Expression |
---|---|
nfinf.1 | |
nfinf.2 | |
nfinf.3 |
Ref | Expression |
---|---|
nfinf | inf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-inf 6944 | . 2 inf | |
2 | nfinf.1 | . . 3 | |
3 | nfinf.2 | . . 3 | |
4 | nfinf.3 | . . . 4 | |
5 | 4 | nfcnv 4780 | . . 3 |
6 | 2, 3, 5 | nfsup 6951 | . 2 |
7 | 1, 6 | nfcxfr 2303 | 1 inf |
Colors of variables: wff set class |
Syntax hints: wnfc 2293 ccnv 4600 csup 6941 infcinf 6942 |
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-3an 969 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-ral 2447 df-rex 2448 df-rab 2451 df-v 2726 df-un 3118 df-sn 3579 df-pr 3580 df-op 3582 df-uni 3787 df-br 3980 df-opab 4041 df-cnv 4609 df-sup 6943 df-inf 6944 |
This theorem is referenced by: (None) |
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