Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > inimasn | Unicode version |
Description: The intersection of the image of singleton (Contributed by Thierry Arnoux, 16-Dec-2017.) |
Ref | Expression |
---|---|
inimasn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elin 3254 | . . 3 | |
2 | elin 3254 | . . . . 5 | |
3 | 2 | a1i 9 | . . . 4 |
4 | vex 2684 | . . . . 5 | |
5 | elimasng 4902 | . . . . 5 | |
6 | 4, 5 | mpan2 421 | . . . 4 |
7 | elimasng 4902 | . . . . . 6 | |
8 | 4, 7 | mpan2 421 | . . . . 5 |
9 | elimasng 4902 | . . . . . 6 | |
10 | 4, 9 | mpan2 421 | . . . . 5 |
11 | 8, 10 | anbi12d 464 | . . . 4 |
12 | 3, 6, 11 | 3bitr4rd 220 | . . 3 |
13 | 1, 12 | syl5rbb 192 | . 2 |
14 | 13 | eqrdv 2135 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 cvv 2681 cin 3065 csn 3522 cop 3525 cima 4537 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-sbc 2905 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-xp 4540 df-cnv 4542 df-dm 4544 df-rn 4545 df-res 4546 df-ima 4547 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |