Theorem leao2 163

Description: L.e. absorption. (Contributed by NM, 8-Jul-2000.)

Assertion

Ref	Expression
leao2	(b ∩ a) ≤ (a ∪ c)

Proof of Theorem leao2

Step	Hyp	Ref	Expression
1		lear 161	. 2 (b ∩ a) ≤ a
2		leo 158	. 2 a ≤ (a ∪ c)
3	1, 2	letr 137	1 (b ∩ a) ≤ (a ∪ c)

Syntax hints:   ≤ wle 2   ∪ wo 6   ∩ wa 7

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  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  df-le2 131

This theorem is referenced by:  bi4  840  negantlem10  861  mhlem1  877  mhlem2  878  mh  879  mhcor1  888  lem4.6.7  1103  vneulem6  1136  vneulem7  1137  vneulemexp  1148  dp32  1196