Theorem ndsubmultl-P7.24d.RC 901

Description: Inference Form of ndsubmultl-P7.24d 854. †

Hypothesis

Ref	Expression
ndsubmultl-P7.24d.RC.1	⊢ 𝑡 = 𝑢

Assertion

Ref	Expression
ndsubmultl-P7.24d.RC	⊢ (𝑡 ⋅ 𝑤) = (𝑢 ⋅ 𝑤)

Proof of Theorem ndsubmultl-P7.24d.RC

Step	Hyp	Ref	Expression
1		ndsubmultl-P7.24d.RC.1	. . . 4 ⊢ 𝑡 = 𝑢
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → 𝑡 = 𝑢)
3	2	ndsubmultl-P7.24d 854	. 2 ⊢ (⊤ → (𝑡 ⋅ 𝑤) = (𝑢 ⋅ 𝑤))
4	3	ndtruee-P3.18 183	1 ⊢ (𝑡 ⋅ 𝑤) = (𝑢 ⋅ 𝑤)

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-multl 25

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)