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Theorem wleran 394
 Description: Add conjunct to right of both sides.
Hypothesis
Ref Expression
wle.1 (a2 b) = 1
Assertion
Ref Expression
wleran ((ac) ≤2 (bc)) = 1

Proof of Theorem wleran
StepHypRef Expression
1 anandir 115 . . . . 5 ((ab) ∩ c) = ((ac) ∩ (bc))
21bi1 118 . . . 4 (((ab) ∩ c) ≡ ((ac) ∩ (bc))) = 1
32wr1 197 . . 3 (((ac) ∩ (bc)) ≡ ((ab) ∩ c)) = 1
4 wle.1 . . . . 5 (a2 b) = 1
54wdf2le2 386 . . . 4 ((ab) ≡ a) = 1
65wran 369 . . 3 (((ab) ∩ c) ≡ (ac)) = 1
73, 6wr2 371 . 2 (((ac) ∩ (bc)) ≡ (ac)) = 1
87wdf2le1 385 1 ((ac) ≤2 (bc)) = 1
 Colors of variables: term Syntax hints:   = wb 1   ∩ wa 7  1wt 8   ≤2 wle2 10 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-wom 361 This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le 129  df-le1 130  df-le2 131 This theorem is referenced by:  wle2an  404
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