Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > pmex | Unicode version |
Description: The class of all partial functions from one set to another is a set. (Contributed by NM, 15-Nov-2007.) |
Ref | Expression |
---|---|
pmex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancom 264 | . . 3 | |
2 | 1 | abbii 2255 | . 2 |
3 | xpexg 4653 | . . 3 | |
4 | abssexg 4106 | . . 3 | |
5 | 3, 4 | syl 14 | . 2 |
6 | 2, 5 | eqeltrid 2226 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1480 cab 2125 cvv 2686 wss 3071 cxp 4537 wfun 5117 |
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-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-opab 3990 df-xp 4545 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |