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Mirrors > Home > MPE Home > Th. List > cbvabvOLD | Structured version Visualization version GIF version |
Description: Obsolete version of cbvabv 2889 as of 9-May-2023. (Contributed by NM, 26-May-1999.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
cbvabvOLD.1 | ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) |
Ref | Expression |
---|---|
cbvabvOLD | ⊢ {𝑥 ∣ 𝜑} = {𝑦 ∣ 𝜓} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1915 | . 2 ⊢ Ⅎ𝑦𝜑 | |
2 | nfv 1915 | . 2 ⊢ Ⅎ𝑥𝜓 | |
3 | cbvabvOLD.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
4 | 1, 2, 3 | cbvab 2891 | 1 ⊢ {𝑥 ∣ 𝜑} = {𝑦 ∣ 𝜓} |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 208 = wceq 1537 {cab 2799 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-13 2390 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2800 df-cleq 2814 |
This theorem is referenced by: (None) |
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