Description: Equality theorem for a product. (Contributed by Scott Fenton, 1-Dec-2017)
Ref | Expression | ||
---|---|---|---|
Assertion | prodeq1 | ⊢ ( 𝐴 = 𝐵 → ∏ 𝑘 ∈ 𝐴 𝐶 = ∏ 𝑘 ∈ 𝐵 𝐶 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv | ⊢ Ⅎ 𝑘 𝐴 | |
2 | nfcv | ⊢ Ⅎ 𝑘 𝐵 | |
3 | 1 2 | prodeq1f | ⊢ ( 𝐴 = 𝐵 → ∏ 𝑘 ∈ 𝐴 𝐶 = ∏ 𝑘 ∈ 𝐵 𝐶 ) |