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Axiom ax-mulcl 6761
Description: Closure law for multiplication of complex numbers. Axiom for real and complex numbers, justified by theorem axmulcl 6732. Proofs should normally use mulcl 6786 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-mulcl ((A B ℂ) → (A · B) ℂ)

Detailed syntax breakdown of Axiom ax-mulcl
StepHypRef Expression
1 cA . . . 4 class A
2 cc 6689 . . . 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 ℂ)
7 cmul 6696 . . . 4 class ·
81, 4, 7co 5455 . . 3 class (A · B)
98, 2wcel 1390 . 2 wff (A · B)
106, 9wi 4 1 wff ((A B ℂ) → (A · B) ℂ)
Colors of variables: wff set class
This axiom is referenced by:  mulcl  6786
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