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Mirrors > Home > ILE Home > Th. List > nff | Unicode version |
Description: Bound-variable hypothesis builder for a mapping. (Contributed by NM, 29-Jan-2004.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
nff.1 | |
nff.2 | |
nff.3 |
Ref | Expression |
---|---|
nff |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-f 5187 | . 2 | |
2 | nff.1 | . . . 4 | |
3 | nff.2 | . . . 4 | |
4 | 2, 3 | nffn 5279 | . . 3 |
5 | 2 | nfrn 4844 | . . . 4 |
6 | nff.3 | . . . 4 | |
7 | 5, 6 | nfss 3131 | . . 3 |
8 | 4, 7 | nfan 1552 | . 2 |
9 | 1, 8 | nfxfr 1461 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wnf 1447 wnfc 2293 wss 3112 crn 4600 wfn 5178 wf 5179 |
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 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-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-v 2724 df-un 3116 df-in 3118 df-ss 3125 df-sn 3577 df-pr 3578 df-op 3580 df-br 3978 df-opab 4039 df-rel 4606 df-cnv 4607 df-co 4608 df-dm 4609 df-rn 4610 df-fun 5185 df-fn 5186 df-f 5187 |
This theorem is referenced by: nff1 5386 |
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