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Mirrors > Home > ILE Home > Th. List > ixpfn | Unicode version |
Description: A nuple is a function. (Contributed by FL, 6-Jun-2011.) (Revised by Mario Carneiro, 31-May-2014.) |
Ref | Expression |
---|---|
ixpfn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fneq1 5181 | . 2 | |
2 | elixp2 6564 | . . 3 | |
3 | 2 | simp2bi 982 | . 2 |
4 | 1, 3 | vtoclga 2726 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1465 wral 2393 cvv 2660 wfn 5088 cfv 5093 cixp 6560 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-iota 5058 df-fun 5095 df-fn 5096 df-fv 5101 df-ixp 6561 |
This theorem is referenced by: ixpprc 6581 ixpssmap2g 6589 ixpssmapg 6590 |
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