oprabss - Intuitionistic Logic Explorer

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Theorem oprabss 5865

Description: Structure of an operation class abstraction. (Contributed by NM, 28-Nov-2006.)

**Assertion**
Ref	Expression
oprabss

(

)

**Proof of Theorem oprabss**
Step	Hyp	Ref	Expression
1		reloprab 5827	. . 3
2		relssdmrn 5067	. . 3
3	1, 2	ax-mp 5	. 2
4		reldmoprab 5864	. . . 4
5		df-rel 4554	. . . 4
6	4, 5	mpbi 144	. . 3
7		ssv 3124	. . 3
8		xpss12 4654	. . 3 $/\$
9	6, 7, 8	mp2an 423	. 2
10	3, 9	sstri 3111	1

Colors of variables: wff set class

Syntax hints:

cvv 2689

wss 3076

cxp 4545

cdm 4547

crn 4548

wrel 4552

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 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139

This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-br 3938 df-opab 3998 df-xp 4553 df-rel 4554 df-cnv 4555 df-dm 4557 df-rn 4558 df-oprab 5786

This theorem is referenced by: (None)