Theorem lei2 346

Description: "Less than" analogue is equal to →₂ implication.

Assertion

Ref	Expression
lei2	(a ≤2 b) = (a →2 b)

Proof of Theorem lei2

Step	Hyp	Ref	Expression
1		mi 125	. 2 ((a ∪ b) ≡ b) = (b ∪ (a⊥ ∩ b⊥ ))
2		df-le 129	. 2 (a ≤2 b) = ((a ∪ b) ≡ b)
3		df-i2 45	. 2 (a →2 b) = (b ∪ (a⊥ ∩ b⊥ ))
4	1, 2, 3	3tr1 63	1 (a ≤2 b) = (a →2 b)

Syntax hints:   = wb 1  ^⊥ wn 4   ≡ tb 5   ∪ wo 6   ∩ wa 7   ≤₂ wle2 10   →₂ wi2 13

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i2 45  df-le 129

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