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Axiom ax-mulass 6746
Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axmulass 6717. Proofs should normally use mulass 6770 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-mulass ((A B 𝐶 ℂ) → ((A · B) · 𝐶) = (A · (B · 𝐶)))

Detailed syntax breakdown of Axiom ax-mulass
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
6 cC . . . 4 class 𝐶
76, 2wcel 1390 . . 3 wff 𝐶
83, 5, 7w3a 884 . 2 wff (A B 𝐶 ℂ)
9 cmul 6676 . . . . 5 class ·
101, 4, 9co 5455 . . . 4 class (A · B)
1110, 6, 9co 5455 . . 3 class ((A · B) · 𝐶)
124, 6, 9co 5455 . . . 4 class (B · 𝐶)
131, 12, 9co 5455 . . 3 class (A · (B · 𝐶))
1411, 13wceq 1242 . 2 wff ((A · B) · 𝐶) = (A · (B · 𝐶))
158, 14wi 4 1 wff ((A B 𝐶 ℂ) → ((A · B) · 𝐶) = (A · (B · 𝐶)))
Colors of variables: wff set class
This axiom is referenced by:  mulass  6770
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