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Mirrors > Home > MPE Home > Th. List > nff1o | Structured version Visualization version Unicode version |
Description: Bound-variable hypothesis builder for a one-to-one onto function. (Contributed by NM, 16-May-2004.) |
Ref | Expression |
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nff1o.1 | |
nff1o.2 | |
nff1o.3 |
Ref | Expression |
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nff1o |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-f1o 5895 | . 2 | |
2 | nff1o.1 | . . . 4 | |
3 | nff1o.2 | . . . 4 | |
4 | nff1o.3 | . . . 4 | |
5 | 2, 3, 4 | nff1 6099 | . . 3 |
6 | 2, 3, 4 | nffo 6114 | . . 3 |
7 | 5, 6 | nfan 1828 | . 2 |
8 | 1, 7 | nfxfr 1779 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wa 384 wnf 1708 wnfc 2751 wf1 5885 wfo 5886 wf1o 5887 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 |
This theorem is referenced by: nfiso 6572 nfsum1 14420 nfsum 14421 nfcprod1 14640 nfcprod 14641 fsumiunle 29575 esumiun 30156 wessf1ornlem 39371 stoweidlem35 40252 |
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