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Theorem wleao 377
 Description: Relation between two methods of expressing "less than or equal to".
Hypothesis
Ref Expression
wleao.1 ((cb) ≡ a) = 1
Assertion
Ref Expression
wleao ((ab) ≡ b) = 1

Proof of Theorem wleao
StepHypRef Expression
1 wa2 192 . . 3 ((ab) ≡ (ba)) = 1
2 wleao.1 . . . . . 6 ((cb) ≡ a) = 1
32wr1 197 . . . . 5 (a ≡ (cb)) = 1
4 wancom 203 . . . . . 6 ((bc) ≡ (cb)) = 1
54wr1 197 . . . . 5 ((cb) ≡ (bc)) = 1
63, 5wr2 371 . . . 4 (a ≡ (bc)) = 1
76wlor 368 . . 3 ((ba) ≡ (b ∪ (bc))) = 1
81, 7wr2 371 . 2 ((ab) ≡ (b ∪ (bc))) = 1
9 wa5b 200 . 2 ((b ∪ (bc)) ≡ b) = 1
108, 9wr2 371 1 ((ab) ≡ b) = 1
 Colors of variables: term Syntax hints:   = wb 1   ≡ tb 5   ∪ wo 6   ∩ wa 7  1wt 8 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-le1 130  df-le2 131 This theorem is referenced by:  wdf2le1  385
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