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Mirrors > Home > MPE Home > Th. List > nfunv | Structured version Visualization version Unicode version |
Description: The universe is not a function. (Contributed by Raph Levien, 27-Jan-2004.) |
Ref | Expression |
---|---|
nfunv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0nelxp 5143 | . . 3 | |
2 | 0ex 4790 | . . . 4 | |
3 | df-rel 5121 | . . . . . 6 | |
4 | 3 | biimpi 206 | . . . . 5 |
5 | 4 | sseld 3602 | . . . 4 |
6 | 2, 5 | mpi 20 | . . 3 |
7 | 1, 6 | mto 188 | . 2 |
8 | funrel 5905 | . 2 | |
9 | 7, 8 | mto 188 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wcel 1990 cvv 3200 wss 3574 c0 3915 cxp 5112 wrel 5119 wfun 5882 |
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 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
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-ne 2795 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-opab 4713 df-xp 5120 df-rel 5121 df-fun 5890 |
This theorem is referenced by: (None) |
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