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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 2384. Use the weaker cbviotavw 6315 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 6316 | 1 ⊢ (℩𝑥𝜑) = (℩𝑦𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 208 = wceq 1531 ℩cio 6305 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1905 ax-6 1964 ax-7 2009 ax-8 2110 ax-9 2118 ax-10 2139 ax-11 2154 ax-12 2170 ax-13 2384 ax-ext 2791 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1534 df-ex 1775 df-nf 1779 df-sb 2064 df-clab 2798 df-cleq 2812 df-clel 2891 df-rex 3142 df-sn 4560 df-uni 4831 df-iota 6307 |
This theorem is referenced by: (None) |
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