Theorem pssdifcom2 3914

Description: Two ways to express non-covering pairs of subsets. (Contributed by Stefan O'Rear, 31-Oct-2014.)

Assertion

Ref	Expression
pssdifcom2

Proof of Theorem pssdifcom2

Step	Hyp	Ref	Expression
1		ssconb 3636	. . . 4
2	1	ancoms 453	. . 3
3		difcom 3912	. . . . 5
4	3	a1i 11	. . . 4
5	4	notbid 294	. . 3
6	2, 5	anbi12d 710	. 2
7		dfpss3 3589	. 2
8		dfpss3 3589	. 2
9	6, 7, 8	3bitr4g 288	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  \cdif 3472  C_wss 3475  C.wpss 3476

This theorem is referenced by:  fin2i2  8719

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-pss 3491