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Mirrors > Home > ILE Home > Th. List > nffn | Unicode version |
Description: Bound-variable hypothesis builder for a function with domain. (Contributed by NM, 30-Jan-2004.) |
Ref | Expression |
---|---|
nffn.1 | |
nffn.2 |
Ref | Expression |
---|---|
nffn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-fn 5201 | . 2 | |
2 | nffn.1 | . . . 4 | |
3 | 2 | nffun 5221 | . . 3 |
4 | 2 | nfdm 4855 | . . . 4 |
5 | nffn.2 | . . . 4 | |
6 | 4, 5 | nfeq 2320 | . . 3 |
7 | 3, 6 | nfan 1558 | . 2 |
8 | 1, 7 | nfxfr 1467 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1348 wnf 1453 wnfc 2299 cdm 4611 wfun 5192 wfn 5193 |
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 3589 df-pr 3590 df-op 3592 df-br 3990 df-opab 4051 df-rel 4618 df-cnv 4619 df-co 4620 df-dm 4621 df-fun 5200 df-fn 5201 |
This theorem is referenced by: nff 5344 nffo 5419 nfixpxy 6695 nfixp1 6696 |
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