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Mirrors > Home > MPE Home > Th. List > cbviotav | Structured version Visualization version GIF version |
Description: Change bound variables in a description binder. (Contributed by Andrew Salmon, 1-Aug-2011.) |
Ref | Expression |
---|---|
cbviotav.1 | ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) |
Ref | Expression |
---|---|
cbviotav | ⊢ (℩𝑥𝜑) = (℩𝑦𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbviotav.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
2 | nfv 1843 | . 2 ⊢ Ⅎ𝑦𝜑 | |
3 | nfv 1843 | . 2 ⊢ Ⅎ𝑥𝜓 | |
4 | 1, 2, 3 | cbviota 5856 | 1 ⊢ (℩𝑥𝜑) = (℩𝑦𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 196 = wceq 1483 ℩cio 5849 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rex 2918 df-sn 4178 df-uni 4437 df-iota 5851 |
This theorem is referenced by: oeeui 7682 ellimciota 39846 fourierdlem96 40419 fourierdlem97 40420 fourierdlem98 40421 fourierdlem99 40422 fourierdlem105 40428 fourierdlem106 40429 fourierdlem108 40431 fourierdlem110 40433 fourierdlem112 40435 fourierdlem113 40436 fourierdlem115 40438 |
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