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Theorem funss 4950

Description: Subclass theorem for function predicate. (Contributed by NM, 16-Aug-1994.) (Proof shortened by Mario Carneiro, 24-Jun-2014.)

**Assertion**
Ref	Expression
funss

**Proof of Theorem funss**
Step	Hyp	Ref	Expression
1		relss 4453	. . 3
2		coss1 4519	. . . . 5
3		cnvss 4536	. . . . . 6
4		coss2 4520	. . . . . 6
5	3, 4	syl 14	. . . . 5
6	2, 5	sstrd 3010	. . . 4
7		sstr2 3007	. . . 4
8	6, 7	syl 14	. . 3
9	1, 8	anim12d 328	. 2 $/\$ $/\$
10		df-fun 4934	. 2 $/\$
11		df-fun 4934	. 2 $/\$
12	9, 10, 11	3imtr4g 203	1

Colors of variables: wff set class

Syntax hints:

wi 4 $/\$ wa 102

wss 2974

cid 4051

ccnv 4370

ccom 4375

wrel 4376

wfun 4926

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2064

This theorem depends on definitions: df-bi 115 df-nf 1391 df-sb 1687 df-clab 2069 df-cleq 2075 df-clel 2078 df-nfc 2209 df-in 2980 df-ss 2987 df-br 3794 df-opab 3848 df-rel 4378 df-cnv 4379 df-co 4380 df-fun 4934

This theorem is referenced by: funeq 4951 funopab4 4967 funres 4971 fun0 4988 funcnvcnv 4989 funin 5001 funres11 5002 foimacnv 5175 tfrlemibfn 5977 tfr1onlembfn 5993 tfrcllembfn 6006