Description: Change bound variable in a directed integral. (Contributed by Mario Carneiro, 7-Sep-2014)
Ref | Expression | ||
---|---|---|---|
Hypothesis | cbvditg.1 | ⊢ ( 𝑥 = 𝑦 → 𝐶 = 𝐷 ) | |
Assertion | cbvditgv | ⊢ ⨜ [ 𝐴 → 𝐵 ] 𝐶 d 𝑥 = ⨜ [ 𝐴 → 𝐵 ] 𝐷 d 𝑦 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvditg.1 | ⊢ ( 𝑥 = 𝑦 → 𝐶 = 𝐷 ) | |
2 | nfcv | ⊢ Ⅎ 𝑦 𝐶 | |
3 | nfcv | ⊢ Ⅎ 𝑥 𝐷 | |
4 | 1 2 3 | cbvditg | ⊢ ⨜ [ 𝐴 → 𝐵 ] 𝐶 d 𝑥 = ⨜ [ 𝐴 → 𝐵 ] 𝐷 d 𝑦 |