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Theorem ml3 1130
Description: Form of modular law that swaps two terms. (Contributed by NM, 1-Apr-2012.)
Assertion
Ref Expression
ml3 (a ∪ (b ∩ (ca))) = (a ∪ (c ∩ (ba)))

Proof of Theorem ml3
StepHypRef Expression
1 ml3le 1129 . 2 (a ∪ (b ∩ (ca))) ≤ (a ∪ (c ∩ (ba)))
2 ml3le 1129 . 2 (a ∪ (c ∩ (ba))) ≤ (a ∪ (b ∩ (ca)))
31, 2lebi 145 1 (a ∪ (b ∩ (ca))) = (a ∪ (c ∩ (ba)))
Colors of variables: term
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
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