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Mirrors > Home > MPE Home > Th. List > nfunv | Structured version Visualization version GIF version |
Description: The universe is not a function. (Contributed by Raph Levien, 27-Jan-2004.) |
Ref | Expression |
---|---|
nfunv | ⊢ ¬ Fun V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nrelv 5524 | . 2 ⊢ ¬ Rel V | |
2 | funrel 6207 | . 2 ⊢ (Fun V → Rel V) | |
3 | 1, 2 | mto 189 | 1 ⊢ ¬ Fun V |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 Vcvv 3415 Rel wrel 5413 Fun wfun 6184 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1758 ax-4 1772 ax-5 1869 ax-6 1928 ax-7 1965 ax-8 2052 ax-9 2059 ax-10 2079 ax-11 2093 ax-12 2106 ax-ext 2750 ax-sep 5061 ax-nul 5068 ax-pr 5187 |
This theorem depends on definitions: df-bi 199 df-an 388 df-or 834 df-3an 1070 df-tru 1510 df-ex 1743 df-nf 1747 df-sb 2016 df-clab 2759 df-cleq 2771 df-clel 2846 df-nfc 2918 df-ne 2968 df-v 3417 df-dif 3834 df-un 3836 df-in 3838 df-ss 3845 df-nul 4181 df-if 4352 df-sn 4443 df-pr 4445 df-op 4449 df-opab 4993 df-xp 5414 df-rel 5415 df-fun 6192 |
This theorem is referenced by: (None) |
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