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Theorem 3vded13 816
 Description: A 3-variable theorem. Experiment with weak deduction theorem.
Hypotheses
Ref Expression
3vded13.1 (b ∩ (c1 a)) ≤ (c1 (b1 a))
3vded13.2 ca
Assertion
Ref Expression
3vded13 c ≤ (b1 a)

Proof of Theorem 3vded13
StepHypRef Expression
1 an1 106 . . . . 5 (b ∩ 1) = b
21ax-r1 35 . . . 4 b = (b ∩ 1)
3 3vded13.2 . . . . . . 7 ca
43u1lemle1 710 . . . . . 6 (c1 a) = 1
54ax-r1 35 . . . . 5 1 = (c1 a)
65lan 77 . . . 4 (b ∩ 1) = (b ∩ (c1 a))
72, 6ax-r2 36 . . 3 b = (b ∩ (c1 a))
8 3vded13.1 . . 3 (b ∩ (c1 a)) ≤ (c1 (b1 a))
97, 8bltr 138 . 2 b ≤ (c1 (b1 a))
1093vded11 814 1 c ≤ (b1 a)
 Colors of variables: term Syntax hints:   ≤ wle 2   ∩ 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  ax-r3 439 This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by: (None)
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