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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 4596 | . . 3 | |
2 | coss1 4664 | . . . . 5 | |
3 | cnvss 4682 | . . . . . 6 | |
4 | coss2 4665 | . . . . . 6 | |
5 | 3, 4 | syl 14 | . . . . 5 |
6 | 2, 5 | sstrd 3077 | . . . 4 |
7 | sstr2 3074 | . . . 4 | |
8 | 6, 7 | syl 14 | . . 3 |
9 | 1, 8 | anim12d 333 | . 2 |
10 | df-fun 5095 | . 2 | |
11 | df-fun 5095 | . 2 | |
12 | 9, 10, 11 | 3imtr4g 204 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wss 3041 cid 4180 ccnv 4508 ccom 4513 wrel 4514 wfun 5087 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-in 3047 df-ss 3054 df-br 3900 df-opab 3960 df-rel 4516 df-cnv 4517 df-co 4518 df-fun 5095 |
This theorem is referenced by: funeq 5113 funopab4 5130 funres 5134 fun0 5151 funcnvcnv 5152 funin 5164 funres11 5165 foimacnv 5353 tfrlemibfn 6193 tfr1onlembfn 6209 tfrcllembfn 6222 strslssd 11932 strle1g 11976 |
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