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Theorem funss 5907

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 5206	. . 3
2		coss1 5277	. . . . 5
3		cnvss 5294	. . . . . 6
4		coss2 5278	. . . . . 6
5	3, 4	syl 17	. . . . 5
6	2, 5	sstrd 3613	. . . 4
7		sstr2 3610	. . . 4
8	6, 7	syl 17	. . 3
9	1, 8	anim12d 586	. 2 $/\$ $/\$
10		df-fun 5890	. 2 $/\$
11		df-fun 5890	. 2 $/\$
12	9, 10, 11	3imtr4g 285	1

Colors of variables: wff setvar class

Syntax hints:

wi 4 $/\$ wa 384

wss 3574

cid 5023

ccnv 5113

ccom 5118

wrel 5119

wfun 5882

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602

This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-in 3581 df-ss 3588 df-br 4654 df-opab 4713 df-rel 5121 df-cnv 5122 df-co 5123 df-fun 5890

This theorem is referenced by: funeq 5908 funopab4 5925 funres 5929 fun0 5954 funcnvcnv 5956 funin 5965 funres11 5966 foimacnv 6154 funsssuppss 7321 strssd 15909 strle1 15973 xpsc0 16220 xpsc1 16221 pjpm 20052 subgrfun 26173 frrlem5c 31786