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Theorem lel2an 171
Description: Conjunction of 2 l.e.'s. (Contributed by NM, 11-Nov-1997.)
Hypotheses
Ref Expression
lel2.1 ab
lel2.2 cb
Assertion
Ref Expression
lel2an (ac) ≤ b

Proof of Theorem lel2an
StepHypRef Expression
1 lel2.1 . . 3 ab
2 lel2.2 . . 3 cb
31, 2le2an 169 . 2 (ac) ≤ (bb)
4 anidm 111 . 2 (bb) = b
53, 4lbtr 139 1 (ac) ≤ b
Colors of variables: term
Syntax hints:  wle 2  wa 7
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
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131
This theorem is referenced by: (None)
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