Theorem oagen2b 1017

Description: "Generalized" OA. (Contributed by NM, 21-Nov-1998.)

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 153	. 2 (d ∩ e) ≤ ((a →2 b) ∩ e)
3		oagen2b.2	. . 3 e ≤ ((b ∪ c) →0 ((a →2 b) ∩ (a →2 c)))
4	3	oagen2 1016	. 2 ((a →2 b) ∩ e) ≤ (a →2 c)
5	2, 4	letr 137	1 (d ∩ e) ≤ (a →2 c)

Syntax hints:   ≤ wle 2   ∪ wo 6   ∩ wa 7   →₀ wi0 11   →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  ax-3oa 998

This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i0 43  df-i1 44  df-i2 45  df-le1 130  df-le2 131

This theorem is referenced by: (None)