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Theorem wql1lem 287
 Description: Classical implication inferred from Sakaki implication. (Contributed by NM, 5-Dec-1998.)
Hypothesis
Ref Expression
wql1lem.1 (a1 b) = 1
Assertion
Ref Expression
wql1lem (ab) = 1

Proof of Theorem wql1lem
StepHypRef Expression
1 le1 146 . 2 (ab) ≤ 1
2 wql1lem.1 . . . 4 (a1 b) = 1
32ax-r1 35 . . 3 1 = (a1 b)
4 df-i1 44 . . . 4 (a1 b) = (a ∪ (ab))
5 lear 161 . . . . 5 (ab) ≤ b
65lelor 166 . . . 4 (a ∪ (ab)) ≤ (ab)
74, 6bltr 138 . . 3 (a1 b) ≤ (ab)
83, 7bltr 138 . 2 1 ≤ (ab)
91, 8lebi 145 1 (ab) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 8   →1 wi1 12 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 This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i1 44  df-le1 130  df-le2 131 This theorem is referenced by:  wql1  293  wdwom  1106
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