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Mirrors > Home > ILE Home > Th. List > nff1o | Unicode version |
Description: Bound-variable hypothesis builder for a one-to-one onto function. (Contributed by NM, 16-May-2004.) |
Ref | Expression |
---|---|
nff1o.1 | |
nff1o.2 | |
nff1o.3 |
Ref | Expression |
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nff1o |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-f1o 5203 | . 2 | |
2 | nff1o.1 | . . . 4 | |
3 | nff1o.2 | . . . 4 | |
4 | nff1o.3 | . . . 4 | |
5 | 2, 3, 4 | nff1 5399 | . . 3 |
6 | 2, 3, 4 | nffo 5417 | . . 3 |
7 | 5, 6 | nfan 1558 | . 2 |
8 | 1, 7 | nfxfr 1467 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wnf 1453 wnfc 2299 wf1 5193 wfo 5194 wf1o 5195 |
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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-sn 3587 df-pr 3588 df-op 3590 df-br 3988 df-opab 4049 df-rel 4616 df-cnv 4617 df-co 4618 df-dm 4619 df-rn 4620 df-fun 5198 df-fn 5199 df-f 5200 df-f1 5201 df-fo 5202 df-f1o 5203 |
This theorem is referenced by: nfiso 5782 nfsum1 11306 nfsum 11307 nfcprod1 11504 nfcprod 11505 |
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