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Theorem wleoa 376
 Description: Relation between two methods of expressing "less than or equal to".
Hypothesis
Ref Expression
wleoa.1 ((ac) ≡ b) = 1
Assertion
Ref Expression
wleoa ((ab) ≡ a) = 1

Proof of Theorem wleoa
StepHypRef Expression
1 wleoa.1 . . . 4 ((ac) ≡ b) = 1
21wr1 197 . . 3 (b ≡ (ac)) = 1
32wlan 370 . 2 ((ab) ≡ (a ∩ (ac))) = 1
4 wa5c 201 . 2 ((a ∩ (ac)) ≡ a) = 1
53, 4wr2 371 1 ((ab) ≡ a) = 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:  wdf2le2  386  wdid0id5  1109  wdid0id1  1110  wdid0id2  1111  wdid0id3  1112  wdid0id4  1113
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