Theorem lerr 142

Description: Add disjunct to right of l.e.

Hypothesis

Ref	Expression
le.1	a ≤ b

Assertion

Ref	Expression
lerr	a ≤ (c ∪ b)

Proof of Theorem lerr

Step	Hyp	Ref	Expression
1		le.1	. . 3 a ≤ b
2	1	ler 141	. 2 a ≤ (b ∪ c)
3		ax-a2 30	. 2 (b ∪ c) = (c ∪ b)
4	2, 3	lbtr 131	1 a ≤ (c ∪ b)

Syntax hints:   ≤ wle 2   ∪ wo 6

This theorem is referenced by:  i3orlem6 539  1oa 802  mhlem 858  marsdenlem3 864  cancellem 873

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-le1 122  df-le2 123

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