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Theorem remulcli 6839
Description: Closure law for multiplication of reals. (Contributed by NM, 17-Jan-1997.)
Hypotheses
Ref Expression
recni.1 A
axri.2 B
Assertion
Ref Expression
remulcli (A · B)

Proof of Theorem remulcli
StepHypRef Expression
1 recni.1 . 2 A
2 axri.2 . 2 B
3 remulcl 6807 . 2 ((A B ℝ) → (A · B) ℝ)
41, 2, 3mp2an 402 1 (A · B)
Colors of variables: wff set class
Syntax hints:   wcel 1390  (class class class)co 5455  cr 6710   · cmul 6716
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101  ax-mulrcl 6782
This theorem is referenced by:  addltmul  7938  nn0lele2xi  8009  numltc  8163
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