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Axiom ax-mulrcl 6782
Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axmulrcl 6753. Proofs should normally use remulcl 6807 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-mulrcl ((A B ℝ) → (A · B) ℝ)

Detailed syntax breakdown of Axiom ax-mulrcl
StepHypRef Expression
1 cA . . . 4 class A
2 cr 6710 . . . 4 class
31, 2wcel 1390 . . 3 wff A
4 cB . . . 4 class B
54, 2wcel 1390 . . 3 wff B
63, 5wa 97 . 2 wff (A B ℝ)
7 cmul 6716 . . . 4 class ·
81, 4, 7co 5455 . . 3 class (A · B)
98, 2wcel 1390 . 2 wff (A · B)
106, 9wi 4 1 wff ((A B ℝ) → (A · B) ℝ)
Colors of variables: wff set class
This axiom is referenced by:  remulcl  6807
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