Theorem oagen2b 997

Description: "Generalized" OA.

Hypotheses

Ref	Expression
oagen2b.1	d ≤ (a →2 b)
oagen2b.2	e ≤ ((b ∪ c) →0 ((a →2 b) ∩ (a →2 c)))

Assertion

Ref	Expression
oagen2b	(d ∩ e) ≤ (a →2 c)

Proof of Theorem oagen2b

Step	Hyp	Ref	Expression
1		oagen2b.1	. . 3 d ≤ (a →2 b)
2	1	leran 145	. 2 (d ∩ e) ≤ ((a →2 b) ∩ e)
3		oagen2b.2	. . 3 e ≤ ((b ∪ c) →0 ((a →2 b) ∩ (a →2 c)))
4	3	oagen2 996	. 2 ((a →2 b) ∩ e) ≤ (a →2 c)
5	2, 4	letr 129	1 (d ∩ e) ≤ (a →2 c)

Syntax hints:   ≤ wle 2   ∪ wo 6   ∩ wa 7   →₀ wi0 12   →₂ wi2 14

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-3oa 978

This theorem depends on definitions:  df-a 39  df-t 40  df-f 41  df-i0 42  df-i1 43  df-i2 44  df-le1 122  df-le2 123

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