Theorem ndsubmultl-P7.24d 854

Description: Natural Deduction: Function Substitution Rule ('⋅' left).

Hypothesis

Ref	Expression
ndsubmultl-P7.24d.1	⊢ (𝛾 → 𝑡 = 𝑢)

Assertion

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

Proof of Theorem ndsubmultl-P7.24d

Step	Hyp	Ref	Expression
1		ndsubmultl-P7.24d.1	. 2 ⊢ (𝛾 → 𝑡 = 𝑢)
2	1	submultl-P5 649	1 ⊢ (𝛾 → (𝑡 ⋅ 𝑤) = (𝑢 ⋅ 𝑤))

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-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:  ndsubmultd-P7  859  ndsubmultl-P7.24d.RC  901  ndsubmultl-P7.24d.CL  921