Axiom ax-L9-multr 26

Description: Right '⋅' substitution.

Assertion

Ref	Expression
ax-L9-multr	⊢ (𝑡 = 𝑢 → (𝑤 ⋅ 𝑡) = (𝑤 ⋅ 𝑢))

Detailed syntax breakdown of Axiom ax-L9-multr

Step	Hyp	Ref	Expression
1		term-t	. . 3 term 𝑡
2		term-u	. . 3 term 𝑢
3	1, 2	wff-equals 6	. 2 wff 𝑡 = 𝑢
4		term-w	. . . 4 term 𝑤
5	4, 1	term-mult 5	. . 3 term (𝑤 ⋅ 𝑡)
6	4, 2	term-mult 5	. . 3 term (𝑤 ⋅ 𝑢)
7	5, 6	wff-equals 6	. 2 wff (𝑤 ⋅ 𝑡) = (𝑤 ⋅ 𝑢)
8	3, 7	wff-imp 10	1 wff (𝑡 = 𝑢 → (𝑤 ⋅ 𝑡) = (𝑤 ⋅ 𝑢))

This axiom is referenced by:  submultr-P5  650