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Mirrors > Home > MPE Home > Th. List > cbvriotavw | Structured version Visualization version GIF version |
Description: Change bound variable in a restricted description binder. Version of cbvriotav 7128 with a disjoint variable condition, which does not require ax-13 2390. (Contributed by NM, 18-Mar-2013.) (Revised by Gino Giotto, 26-Jan-2024.) |
Ref | Expression |
---|---|
cbvriotavw.1 | ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) |
Ref | Expression |
---|---|
cbvriotavw | ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑦 ∈ 𝐴 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1915 | . 2 ⊢ Ⅎ𝑦𝜑 | |
2 | nfv 1915 | . 2 ⊢ Ⅎ𝑥𝜓 | |
3 | cbvriotavw.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
4 | 1, 2, 3 | cbvriotaw 7123 | 1 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑦 ∈ 𝐴 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 208 = wceq 1537 ℩crio 7113 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-v 3496 df-in 3943 df-ss 3952 df-sn 4568 df-uni 4839 df-iota 6314 df-riota 7114 |
This theorem is referenced by: ordtypecbv 8981 fin23lem27 9750 zorn2g 9925 uspgredg2v 27006 usgredg2v 27009 cnlnadji 29853 nmopadjlei 29865 cvmliftlem15 32545 cvmliftiota 32548 cvmlift2 32563 cvmlift3lem7 32572 cvmlift3 32575 lshpkrlem3 36263 cdleme40v 37620 lcfl7N 38652 lcf1o 38702 lcfrlem39 38732 hdmap1cbv 38953 wessf1ornlem 41494 fourierdlem103 42543 fourierdlem104 42544 |
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