Theorem ml3 1130

Description: Form of modular law that swaps two terms. (Contributed by NM, 1-Apr-2012.)

Assertion

Ref	Expression
ml3	(a ∪ (b ∩ (c ∪ a))) = (a ∪ (c ∩ (b ∪ a)))

Proof of Theorem ml3

Step	Hyp	Ref	Expression
1		ml3le 1129	. 2 (a ∪ (b ∩ (c ∪ a))) ≤ (a ∪ (c ∩ (b ∪ a)))
2		ml3le 1129	. 2 (a ∪ (c ∩ (b ∪ a))) ≤ (a ∪ (b ∩ (c ∪ a)))
3	1, 2	lebi 145	1 (a ∪ (b ∩ (c ∪ a))) = (a ∪ (c ∩ (b ∪ a)))

Syntax hints:   = wb 1   ∪ 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  ax-ml 1122

This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131

This theorem is referenced by:  dp41lemg  1189  dp41lemj  1191  xdp41  1198  xxdp41  1201  xdp45lem  1204  xdp43lem  1205  xdp45  1206  xdp43  1207  3dp43  1208