Theorem ler2or 164

Description: Disjunction of 2 l.e.'s

Hypotheses

Ref	Expression
ler2.1	a ≤ b
ler2.2	a ≤ c

Assertion

Ref	Expression
ler2or	a ≤ (b ∪ c)

Proof of Theorem ler2or

Step	Hyp	Ref	Expression
1		oridm 102	. . 3 (a ∪ a) = a
2	1	ax-r1 34	. 2 a = (a ∪ a)
3		ler2.1	. . 3 a ≤ b
4		ler2.2	. . 3 a ≤ c
5	3, 4	le2or 160	. 2 (a ∪ a) ≤ (b ∪ c)
6	2, 5	bltr 130	1 a ≤ (b ∪ c)

Syntax hints:   ≤ wle 2   ∪ wo 6

This theorem is referenced by:  distid 869

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

This theorem depends on definitions:  df-a 39  df-t 40  df-f 41  df-le1 122  df-le2 123

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