Theorem lel2an 163

Description: Conjunction of 2 l.e.'s

Hypotheses

Ref	Expression
lel2.1	a ≤ b
lel2.2	c ≤ b

Assertion

Ref	Expression
lel2an	(a ∩ c) ≤ b

Proof of Theorem lel2an

Step	Hyp	Ref	Expression
1		lel2.1	. . 3 a ≤ b
2		lel2.2	. . 3 c ≤ b
3	1, 2	le2an 161	. 2 (a ∩ c) ≤ (b ∩ b)
4		anidm 103	. 2 (b ∩ b) = b
5	3, 4	lbtr 131	1 (a ∩ c) ≤ b

Syntax hints:   ≤ wle 2   ∩ wa 7

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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