Theorem wdf2le2 386

Description: Alternate definition of "less than or equal to". (Contributed by NM, 27-Sep-1997.)

Hypothesis

Ref	Expression
wdf2le2.1	(a ≤2 b) = 1

Assertion

Ref	Expression
wdf2le2	((a ∩ b) ≡ a) = 1

Proof of Theorem wdf2le2

Step	Hyp	Ref	Expression
1		wdf2le2.1	. . 3 (a ≤2 b) = 1
2	1	wdf-le2 379	. 2 ((a ∪ b) ≡ b) = 1
3	2	wleoa 376	1 ((a ∩ b) ≡ a) = 1

Syntax hints:   = wb 1   ≡ tb 5   ∩ 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:  wlel  392  wleran  394  wlbtr  398  wlecom  409