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Theorem wle2an 404
 Description: Conjunction of 2 l.e.'s.
Hypotheses
Ref Expression
wle2.1 (a2 b) = 1
wle2.2 (c2 d) = 1
Assertion
Ref Expression
wle2an ((ac) ≤2 (bd)) = 1

Proof of Theorem wle2an
StepHypRef Expression
1 wle2.1 . . 3 (a2 b) = 1
21wleran 394 . 2 ((ac) ≤2 (bc)) = 1
3 wle2.2 . . . 4 (c2 d) = 1
43wleran 394 . . 3 ((cb) ≤2 (db)) = 1
5 ancom 74 . . . 4 (bc) = (cb)
65bi1 118 . . 3 ((bc) ≡ (cb)) = 1
7 ancom 74 . . . 4 (bd) = (db)
87bi1 118 . . 3 ((bd) ≡ (db)) = 1
94, 6, 8wle3tr1 399 . 2 ((bc) ≤2 (bd)) = 1
102, 9wletr 396 1 ((ac) ≤2 (bd)) = 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:  wledi  405  wledio  406  wlem14  430
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