cdlemkuu - Mathbox for Norm Megill

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Theorem cdlemkuu 36183

Description: Convert between function and operation forms of

. TODO: Use operation form everywhere. (Contributed by NM, 6-Jul-2013.)

**Hypotheses**
Ref	Expression
cdlemk3.b
cdlemk3.l
cdlemk3.j	$.\/$
cdlemk3.m	$./\$
cdlemk3.a
cdlemk3.h
cdlemk3.t
cdlemk3.r
cdlemk3.s	$.\/$ $./\$ $.\/$
cdlemk3.u1	$.\/$ $./\$ $.\/$
cdlemk3.o2
cdlemk3.u2	$.\/$ $./\$ $.\/$

**Assertion**
Ref	Expression
cdlemkuu	$/\$

Distinct variable groups:

, $./\$

$.\/$ ,

Allowed substitution hints:

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) $.\/$ (

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) $./\$ (

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**Proof of Theorem cdlemkuu**
Step	Hyp	Ref	Expression
1		fveq2 6191	. . . . . . . . 9
2		cdlemk3.o2	. . . . . . . . 9
3	1, 2	syl6eqr 2674	. . . . . . . 8
4	3	fveq1d 6193	. . . . . . 7
5		cnveq 5296	. . . . . . . . 9
6	5	coeq2d 5284	. . . . . . . 8
7	6	fveq2d 6195	. . . . . . 7
8	4, 7	oveq12d 6668	. . . . . 6 $.\/$ $.\/$
9	8	oveq2d 6666	. . . . 5 $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$
10	9	eqeq2d 2632	. . . 4 $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$
11	10	riotabidv 6613	. . 3 $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$
12		fveq2 6191	. . . . . . 7
13	12	oveq2d 6666	. . . . . 6 $.\/$ $.\/$
14		coeq1 5279	. . . . . . . 8
15	14	fveq2d 6195	. . . . . . 7
16	15	oveq2d 6666	. . . . . 6 $.\/$ $.\/$
17	13, 16	oveq12d 6668	. . . . 5 $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$
18	17	eqeq2d 2632	. . . 4 $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$
19	18	riotabidv 6613	. . 3 $.\/$ $./\$ $.\/$ $.\/$ $./\$ $.\/$
20		cdlemk3.u1	. . 3 $.\/$ $./\$ $.\/$
21		riotaex 6615	. . 3 $.\/$ $./\$ $.\/$
22	11, 19, 20, 21	ovmpt2 6796	. 2 $/\$ $.\/$ $./\$ $.\/$
23		cdlemk3.b	. . . 4
24		cdlemk3.l	. . . 4
25		cdlemk3.j	. . . 4 $.\/$
26		cdlemk3.a	. . . 4
27		cdlemk3.h	. . . 4
28		cdlemk3.t	. . . 4
29		cdlemk3.r	. . . 4
30		cdlemk3.m	. . . 4 $./\$
31		cdlemk3.u2	. . . 4 $.\/$ $./\$ $.\/$
32	23, 24, 25, 26, 27, 28, 29, 30, 31	cdlemksv 36132	. . 3 $.\/$ $./\$ $.\/$
33	32	adantl 482	. 2 $/\$ $.\/$ $./\$ $.\/$
34	22, 33	eqtr4d 2659	1 $/\$

Colors of variables: wff setvar class

Syntax hints:

wi 4 $/\$ wa 384

wceq 1483

wcel 1990

cmpt 4729

ccnv 5113

ccom 5118

cfv 5888

crio 6610 (class class class)co 6650

cmpt2 6652

cbs 15857

cple 15948

cjn 16944

cmee 16945

catm 34550

clh 35270

cltrn 35387

ctrl 35445

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 ax-sep 4781 ax-nul 4789 ax-pr 4906

This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-riota 6611 df-ov 6653 df-oprab 6654 df-mpt2 6655

This theorem is referenced by: cdlemk31 36184 cdlemkuel-3 36186 cdlemkuv2-3N 36187 cdlemk18-3N 36188 cdlemk22-3 36189 cdlemkyu 36215

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