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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. Usage of this theorem is discouraged because it depends on ax-13 2366. Use the weaker cbviotavw 6513 when possible. (Contributed by Andrew Salmon, 1-Aug-2011.) (New usage is discouraged.) |
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 1909 | . 2 ⊢ Ⅎ𝑦𝜑 | |
3 | nfv 1909 | . 2 ⊢ Ⅎ𝑥𝜓 | |
4 | 1, 2, 3 | cbviota 6515 | 1 ⊢ (℩𝑥𝜑) = (℩𝑦𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 = wceq 1533 ℩cio 6503 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2166 ax-13 2366 ax-ext 2699 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-tru 1536 df-ex 1774 df-nf 1778 df-sb 2060 df-clab 2706 df-cleq 2720 df-clel 2806 df-v 3475 df-in 3956 df-ss 3966 df-sn 4633 df-uni 4913 df-iota 6505 |
This theorem is referenced by: (None) |
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