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Mirrors > Home > MPE Home > Th. List > cbvriotav | Structured version Visualization version GIF version |
Description: Change bound variable in a restricted description binder. (Contributed by NM, 18-Mar-2013.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
cbvriotav.1 | ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) |
Ref | Expression |
---|---|
cbvriotav | ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑦 ∈ 𝐴 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1830 | . 2 ⊢ Ⅎ𝑦𝜑 | |
2 | nfv 1830 | . 2 ⊢ Ⅎ𝑥𝜓 | |
3 | cbvriotav.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
4 | 1, 2, 3 | cbvriota 6521 | 1 ⊢ (℩𝑥 ∈ 𝐴 𝜑) = (℩𝑦 ∈ 𝐴 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 195 = wceq 1475 ℩crio 6510 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-rex 2902 df-sn 4126 df-uni 4373 df-iota 5768 df-riota 6511 |
This theorem is referenced by: ordtypecbv 8305 fin23lem27 9033 zorn2g 9208 usgraidx2v 25922 cnlnadji 28319 nmopadjlei 28331 cvmliftlem15 30534 cvmliftiota 30537 cvmlift2 30552 cvmlift3lem7 30561 cvmlift3 30564 lshpkrlem3 33417 cdleme40v 34775 lcfl7N 35808 lcf1o 35858 lcfrlem39 35888 hdmap1cbv 36110 wessf1ornlem 38366 fourierdlem103 39102 fourierdlem104 39103 uspgredg2v 40451 usgredg2v 40454 |
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