Theorem df2le1 135

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

Hypothesis

Ref	Expression
df2le1.1	(a ∩ b) = a

Assertion

Ref	Expression
df2le1	a ≤ b

Proof of Theorem df2le1

Step	Hyp	Ref	Expression
1		df2le1.1	. . 3 (a ∩ b) = a
2	1	leao 124	. 2 (a ∪ b) = b
3	2	df-le1 130	1 a ≤ b

Syntax hints:   = wb 1   ≤ wle 2   ∩ wa 7

This theorem was proved from axioms:  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40  df-le1 130

This theorem is referenced by:  letr  137  lbtr  139  lel  151  leran  153  lecon  154  leo  158  i3le  515  u1lemle2  715  u2lemle2  716  u4lemle2  718  u5lemle2  719  bi4  840  gomaex3lem2  915