Theorem leao3 164

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

Assertion

Ref	Expression
leao3	(a ∩ b) ≤ (c ∪ a)

Proof of Theorem leao3

Step	Hyp	Ref	Expression
1		lea 160	. 2 (a ∩ b) ≤ a
2		leor 159	. 2 a ≤ (c ∪ a)
3	1, 2	letr 137	1 (a ∩ b) ≤ (c ∪ a)

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:  mhlem2  878  mh  879  marsdenlem4  883  mhcor1  888  vneulem6  1136  vneulemexp  1148  dp41lemh  1190  dp41lemk  1192  xdp41  1198  xxdp41  1201  xdp45lem  1204  xdp43lem  1205  xdp45  1206  xdp43  1207  3dp43  1208