| Mathbox for Gino Giotto |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > Mathboxes > ditgeq12i | Structured version Visualization version GIF version | ||
| Description: Equality inference for the directed integral. (Contributed by GG, 1-Sep-2025.) |
| Ref | Expression |
|---|---|
| ditgeq12i.1 | ⊢ 𝐴 = 𝐵 |
| ditgeq12i.2 | ⊢ 𝐶 = 𝐷 |
| Ref | Expression |
|---|---|
| ditgeq12i | ⊢ ⨜[𝐴 → 𝐶]𝐸 d𝑥 = ⨜[𝐵 → 𝐷]𝐸 d𝑥 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ditgeq12i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
| 2 | ditgeq12i.2 | . 2 ⊢ 𝐶 = 𝐷 | |
| 3 | eqid 2736 | . 2 ⊢ 𝐸 = 𝐸 | |
| 4 | 1, 2, 3 | ditgeq123i 36188 | 1 ⊢ ⨜[𝐴 → 𝐶]𝐸 d𝑥 = ⨜[𝐵 → 𝐷]𝐸 d𝑥 |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 ⨜cdit 25871 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2707 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-sb 2065 df-clab 2714 df-cleq 2728 df-clel 2815 df-ral 3061 df-rex 3070 df-rab 3436 df-v 3481 df-sbc 3788 df-csb 3899 df-dif 3953 df-un 3955 df-in 3957 df-ss 3967 df-nul 4333 df-if 4525 df-sn 4625 df-pr 4627 df-op 4631 df-uni 4906 df-br 5142 df-opab 5204 df-mpt 5224 df-xp 5689 df-cnv 5691 df-co 5692 df-dm 5693 df-rn 5694 df-res 5695 df-ima 5696 df-pred 6319 df-iota 6512 df-fv 6567 df-ov 7432 df-oprab 7433 df-mpo 7434 df-frecs 8302 df-wrecs 8333 df-recs 8407 df-rdg 8446 df-neg 11491 df-seq 14039 df-sum 15719 df-itg 25648 df-ditg 25872 |
| This theorem is referenced by: (None) |
| Copyright terms: Public domain | W3C validator |