Theorem ndsubmultr-P7.24e.CL 922

Description: Closed Form of ndsubmultr-P7.24e 855. †

Assertion

Ref	Expression
ndsubmultr-P7.24e.CL	⊢ (𝑡 = 𝑢 → (𝑤 ⋅ 𝑡) = (𝑤 ⋅ 𝑢))

Proof of Theorem ndsubmultr-P7.24e.CL

Step	Hyp	Ref	Expression
1		rcp-NDASM1of1 192	. 2 ⊢ (𝑡 = 𝑢 → 𝑡 = 𝑢)
2	1	ndsubmultr-P7.24e 855	1 ⊢ (𝑡 = 𝑢 → (𝑤 ⋅ 𝑡) = (𝑤 ⋅ 𝑢))

Syntax hints:   ⋅ term-mult 5   = wff-equals 6   → wff-imp 10

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14  ax-L9-multr 26

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-true-D2.4 155

This theorem is referenced by:  example-E7.1a  1074