![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 2013 | . 2 ⊢ Ⅎ𝑦𝜑 | |
3 | nfv 2013 | . 2 ⊢ Ⅎ𝑥𝜓 | |
4 | 1, 2, 3 | cbviota 6095 | 1 ⊢ (℩𝑥𝜑) = (℩𝑦𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 198 = wceq 1656 ℩cio 6088 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1894 ax-4 1908 ax-5 2009 ax-6 2075 ax-7 2112 ax-9 2173 ax-10 2192 ax-11 2207 ax-12 2220 ax-13 2389 ax-ext 2803 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 879 df-tru 1660 df-ex 1879 df-nf 1883 df-sb 2068 df-clab 2812 df-cleq 2818 df-clel 2821 df-nfc 2958 df-rex 3123 df-sn 4400 df-uni 4661 df-iota 6090 |
This theorem is referenced by: oeeui 7954 ellimciota 40635 fourierdlem96 41207 fourierdlem97 41208 fourierdlem98 41209 fourierdlem99 41210 fourierdlem105 41216 fourierdlem106 41217 fourierdlem108 41219 fourierdlem110 41221 fourierdlem112 41223 fourierdlem113 41224 fourierdlem115 41226 funressndmafv2rn 42119 |
Copyright terms: Public domain | W3C validator |