![]() |
Mathbox for Stefan O'Rear |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > axac10 | Structured version Visualization version GIF version |
Description: Characterization of choice similar to dffin1-5 9411. (Contributed by Stefan O'Rear, 6-Jan-2015.) |
Ref | Expression |
---|---|
axac10 | ⊢ ( ≈ “ On) = V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axac3 9487 | . 2 ⊢ CHOICE | |
2 | dfac10b 9162 | . 2 ⊢ (CHOICE ↔ ( ≈ “ On) = V) | |
3 | 1, 2 | mpbi 220 | 1 ⊢ ( ≈ “ On) = V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1631 Vcvv 3351 “ cima 5252 Oncon0 5866 ≈ cen 8105 CHOICEwac 9137 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1870 ax-4 1885 ax-5 1991 ax-6 2057 ax-7 2093 ax-8 2147 ax-9 2154 ax-10 2174 ax-11 2190 ax-12 2203 ax-13 2408 ax-ext 2751 ax-rep 4904 ax-sep 4915 ax-nul 4923 ax-pow 4974 ax-pr 5034 ax-un 7095 ax-ac2 9486 |
This theorem depends on definitions: df-bi 197 df-an 383 df-or 827 df-3or 1072 df-3an 1073 df-tru 1634 df-ex 1853 df-nf 1858 df-sb 2050 df-eu 2622 df-mo 2623 df-clab 2758 df-cleq 2764 df-clel 2767 df-nfc 2902 df-ne 2944 df-ral 3066 df-rex 3067 df-reu 3068 df-rmo 3069 df-rab 3070 df-v 3353 df-sbc 3588 df-csb 3683 df-dif 3726 df-un 3728 df-in 3730 df-ss 3737 df-pss 3739 df-nul 4064 df-if 4226 df-pw 4299 df-sn 4317 df-pr 4319 df-tp 4321 df-op 4323 df-uni 4575 df-int 4612 df-iun 4656 df-br 4787 df-opab 4847 df-mpt 4864 df-tr 4887 df-id 5157 df-eprel 5162 df-po 5170 df-so 5171 df-fr 5208 df-se 5209 df-we 5210 df-xp 5255 df-rel 5256 df-cnv 5257 df-co 5258 df-dm 5259 df-rn 5260 df-res 5261 df-ima 5262 df-pred 5823 df-ord 5869 df-on 5870 df-suc 5872 df-iota 5994 df-fun 6033 df-fn 6034 df-f 6035 df-f1 6036 df-fo 6037 df-f1o 6038 df-fv 6039 df-isom 6040 df-riota 6753 df-wrecs 7558 df-recs 7620 df-en 8109 df-card 8964 df-ac 9138 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |