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Theorem wlbtr 398
Description: Transitive inference.
Hypotheses
Ref Expression
wlbtr.1 (a =<2 b) = 1
wlbtr.2 (b == c) = 1
Assertion
Ref Expression
wlbtr (a =<2 c) = 1
Proof of Theorem wlbtr
StepHypRef Expression
1 wlbtr.2 . . . . 5 (b == c) = 1
21wr1 197 . . . 4 (c == b) = 1
32wlan 370 . . 3 ((a ^ c) == (a ^ b)) = 1
4 wlbtr.1 . . . 4 (a =<2 b) = 1
54wdf2le2 386 . . 3 ((a ^ b) == a) = 1
63, 5wr2 371 . 2 ((a ^ c) == a) = 1
76wdf2le1 385 1 (a =<2 c) = 1
Colors of variables: term
Syntax hints:   = wb 1   == tb 5   ^ 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:  wle3tr1  399  wledi  405  wledio  406  ska4  433
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