Theorem ndsubmultr-P7.24e.RC 902

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

Hypothesis

Ref	Expression
ndsubmultr-P7.24e.RC.1	⊢ 𝑡 = 𝑢

Assertion

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

Proof of Theorem ndsubmultr-P7.24e.RC

Step	Hyp	Ref	Expression
1		ndsubmultr-P7.24e.RC.1	. . . 4 ⊢ 𝑡 = 𝑢
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → 𝑡 = 𝑢)
3	2	ndsubmultr-P7.24e 855	. 2 ⊢ (⊤ → (𝑤 ⋅ 𝑡) = (𝑤 ⋅ 𝑢))
4	3	ndtruee-P3.18 183	1 ⊢ (𝑤 ⋅ 𝑡) = (𝑤 ⋅ 𝑢)

Syntax hints:   ⋅ term-mult 5   = wff-equals 6  ⊤wff-true 153

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: (None)