Theorem wlea 388

Description: L.e. absorption. (Contributed by NM, 27-Sep-1997.)

Assertion

Ref	Expression
wlea	((a ∩ b) ≤2 a) = 1

Proof of Theorem wlea

Step	Hyp	Ref	Expression
1		wa2 192	. . 3 (((a ∩ b) ∪ a) ≡ (a ∪ (a ∩ b))) = 1
2		wa5b 200	. . 3 ((a ∪ (a ∩ b)) ≡ a) = 1
3	1, 2	wr2 371	. 2 (((a ∩ b) ∪ a) ≡ a) = 1
4	3	wdf-le1 378	1 ((a ∩ b) ≤2 a) = 1

Syntax hints:   = wb 1   ∪ wo 6   ∩ wa 7  1wt 8   ≤₂ wle2 10

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-wom 361

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le 129  df-le1 130  df-le2 131

This theorem is referenced by:  wledi  405  wcoman1  413  wcom3i  422  ska4  433