ispsubsp2 - Mathbox for Norm Megill

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Theorem ispsubsp2 35032

Description: The predicate "is a projective subspace". (Contributed by NM, 13-Jan-2012.)

**Assertion**
Ref	Expression
ispsubsp2	$/\$ $.\/$

(

)

(

) $.\/$ (

)

(

)

**Proof of Theorem ispsubsp2**
Step	Hyp	Ref	Expression
1		psubspset.l	. . 3
2		psubspset.j	. . 3 $.\/$
3		psubspset.a	. . 3
4		psubspset.s	. . 3
5	1, 2, 3, 4	ispsubsp 35031	. 2 $/\$ $.\/$
6		ralcom 3098	. . . . . . 7 $.\/$ $.\/$
7		r19.23v 3023	. . . . . . . 8 $.\/$ $.\/$
8	7	ralbii 2980	. . . . . . 7 $.\/$ $.\/$
9	6, 8	bitri 264	. . . . . 6 $.\/$ $.\/$
10	9	ralbii 2980	. . . . 5 $.\/$ $.\/$
11		ralcom 3098	. . . . . 6 $.\/$ $.\/$
12		r19.23v 3023	. . . . . . 7 $.\/$ $.\/$
13	12	ralbii 2980	. . . . . 6 $.\/$ $.\/$
14	11, 13	bitri 264	. . . . 5 $.\/$ $.\/$
15	10, 14	bitri 264	. . . 4 $.\/$ $.\/$
16	15	a1i 11	. . 3 $.\/$ $.\/$
17	16	anbi2d 740	. 2 $/\$ $.\/$ $/\$ $.\/$
18	5, 17	bitrd 268	1 $/\$ $.\/$

Colors of variables: wff setvar class

Syntax hints:

wi 4

wb 196 $/\$ wa 384

wceq 1483

wcel 1990

wral 2912

wrex 2913

wss 3574 class class class wbr 4653

cfv 5888 (class class class)co 6650

cple 15948

cjn 16944

catm 34550

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-pow 4843 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-pw 4160 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-ov 6653 df-psubsp 34789

This theorem is referenced by: psubspi 35033 paddclN 35128