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Axiom ax-mulcom 6744
Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by theorem axmulcom 6715. Proofs should normally use mulcom 6768 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-mulcom ((A B ℂ) → (A · B) = (B · A))

Detailed syntax breakdown of Axiom ax-mulcom
StepHypRef Expression
1 cA . . . 4 class A
2 cc 6669 . . . 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 6676 . . . 4 class ·
81, 4, 7co 5455 . . 3 class (A · B)
94, 1, 7co 5455 . . 3 class (B · A)
108, 9wceq 1242 . 2 wff (A · B) = (B · A)
116, 10wi 4 1 wff ((A B ℂ) → (A · B) = (B · A))
Colors of variables: wff set class
This axiom is referenced by:  mulcom  6768
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