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 4696 | . . 3 | |
2 | coss1 4764 | . . . . 5 | |
3 | cnvss 4782 | . . . . . 6 | |
4 | coss2 4765 | . . . . . 6 | |
5 | 3, 4 | syl 14 | . . . . 5 |
6 | 2, 5 | sstrd 3157 | . . . 4 |
7 | sstr2 3154 | . . . 4 | |
8 | 6, 7 | syl 14 | . . 3 |
9 | 1, 8 | anim12d 333 | . 2 |
10 | df-fun 5198 | . 2 | |
11 | df-fun 5198 | . 2 | |
12 | 9, 10, 11 | 3imtr4g 204 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wss 3121 cid 4271 ccnv 4608 ccom 4613 wrel 4614 wfun 5190 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-in 3127 df-ss 3134 df-br 3988 df-opab 4049 df-rel 4616 df-cnv 4617 df-co 4618 df-fun 5198 |
This theorem is referenced by: funeq 5216 funopab4 5233 funres 5237 fun0 5254 funcnvcnv 5255 funin 5267 funres11 5268 foimacnv 5458 tfrlemibfn 6304 tfr1onlembfn 6320 tfrcllembfn 6333 strslssd 12449 strle1g 12494 |
Copyright terms: Public domain | W3C validator |