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Theorem dfpss3 3355

Description: Alternate definition of proper subclass. (Contributed by NM, 7-Feb-1996.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)

**Assertion**
Ref	Expression
dfpss3	$/\$

**Proof of Theorem dfpss3**
Step	Hyp	Ref	Expression
1		dfpss2 3354	. 2 $/\$
2		eqss 3287	. . . . 5 $/\$
3	2	baib 871	. . . 4
4	3	notbid 285	. . 3
5	4	pm5.32i 618	. 2 $/\$ $/\$
6	1, 5	bitri 240	1 $/\$

Colors of variables: wff setvar class

Syntax hints:

wn 3

wb 176 $/\$ wa 358

wceq 1642

wss 3257

wpss 3258

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334

This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-ss 3259 df-pss 3261

This theorem is referenced by: pssirr 3369 pssn2lp 3370 ssnpss 3372 nsspssun 3488 npss0 3589 pssdifcom1 3635 pssdifcom2 3636 dfpss4 3888