| Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > ILE Home > Th. List > funss | Unicode version | ||
| Description: Subclass theorem for function predicate. (Contributed by NM, 16-Aug-1994.) (Proof shortened by Mario Carneiro, 24-Jun-2014.) |
| Ref | Expression |
|---|---|
| funss |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | relss 4762 |
. . 3
| |
| 2 | coss1 4833 |
. . . . 5
| |
| 3 | cnvss 4851 |
. . . . . 6
| |
| 4 | coss2 4834 |
. . . . . 6
| |
| 5 | 3, 4 | syl 14 |
. . . . 5
|
| 6 | 2, 5 | sstrd 3203 |
. . . 4
|
| 7 | sstr2 3200 |
. . . 4
| |
| 8 | 6, 7 | syl 14 |
. . 3
|
| 9 | 1, 8 | anim12d 335 |
. 2
|
| 10 | df-fun 5273 |
. 2
| |
| 11 | df-fun 5273 |
. 2
| |
| 12 | 9, 10, 11 | 3imtr4g 205 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 711 ax-5 1470 ax-7 1471 ax-gen 1472 ax-ie1 1516 ax-ie2 1517 ax-8 1527 ax-10 1528 ax-11 1529 ax-i12 1530 ax-bndl 1532 ax-4 1533 ax-17 1549 ax-i9 1553 ax-ial 1557 ax-i5r 1558 ax-ext 2187 |
| This theorem depends on definitions: df-bi 117 df-nf 1484 df-sb 1786 df-clab 2192 df-cleq 2198 df-clel 2201 df-nfc 2337 df-in 3172 df-ss 3179 df-br 4045 df-opab 4106 df-rel 4682 df-cnv 4683 df-co 4684 df-fun 5273 |
| This theorem is referenced by: funeq 5291 funopab4 5308 funres 5312 fun0 5332 funcnvcnv 5333 funin 5345 funres11 5346 foimacnv 5540 tfrlemibfn 6414 tfr1onlembfn 6430 tfrcllembfn 6443 strslssd 12879 strle1g 12938 |
| Copyright terms: Public domain | W3C validator |