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| Description: Change bound variables in a description binder. Usage of this theorem is discouraged because it depends on ax-13 2376. Use the weaker cbviotavw 6521 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 1913 | . 2 ⊢ Ⅎ𝑦𝜑 | |
| 3 | nfv 1913 | . 2 ⊢ Ⅎ𝑥𝜓 | |
| 4 | 1, 2, 3 | cbviota 6522 | 1 ⊢ (℩𝑥𝜑) = (℩𝑦𝜓) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ↔ wb 206 = wceq 1539 ℩cio 6511 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-10 2140 ax-11 2156 ax-12 2176 ax-13 2376 ax-ext 2707 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1542 df-ex 1779 df-nf 1783 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-v 3481 df-ss 3967 df-sn 4626 df-uni 4907 df-iota 6513 | 
| This theorem is referenced by: (None) | 
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