Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 5121 | . 2 | |
2 | nffn.1 | . . . 4 | |
3 | 2 | nffun 5141 | . . 3 |
4 | 2 | nfdm 4778 | . . . 4 |
5 | nffn.2 | . . . 4 | |
6 | 4, 5 | nfeq 2287 | . . 3 |
7 | 3, 6 | nfan 1544 | . 2 |
8 | 1, 7 | nfxfr 1450 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wceq 1331 wnf 1436 wnfc 2266 cdm 4534 wfun 5112 wfn 5113 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-fun 5120 df-fn 5121 |
This theorem is referenced by: nff 5264 nffo 5339 nfixpxy 6604 nfixp1 6605 |
Copyright terms: Public domain | W3C validator |