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Theorem wle3tr1 399
 Description: Transitive inference useful for introducing definitions.
Hypotheses
Ref Expression
wle3tr1.1 (a2 b) = 1
wle3tr1.2 (ca) = 1
wle3tr1.3 (db) = 1
Assertion
Ref Expression
wle3tr1 (c2 d) = 1

Proof of Theorem wle3tr1
StepHypRef Expression
1 wle3tr1.2 . . 3 (ca) = 1
2 wle3tr1.1 . . 3 (a2 b) = 1
31, 2wbltr 397 . 2 (c2 b) = 1
4 wle3tr1.3 . . 3 (db) = 1
54wr1 197 . 2 (bd) = 1
63, 5wlbtr 398 1 (c2 d) = 1
 Colors of variables: term Syntax hints:   = wb 1   ≡ tb 5  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:  wle3tr2  400  wle2or  403  wle2an  404
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