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Mirrors > Home > MPE Home > Th. List > cbvreuvwOLD | Structured version Visualization version GIF version |
Description: Obsolete version of cbvreuvw 3399 as of 30-Sep-2024. (Contributed by NM, 5-Apr-2004.) (Revised by Gino Giotto, 10-Jan-2024.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
cbvreuvwOLD.1 | ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) |
Ref | Expression |
---|---|
cbvreuvwOLD | ⊢ (∃!𝑥 ∈ 𝐴 𝜑 ↔ ∃!𝑦 ∈ 𝐴 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1916 | . 2 ⊢ Ⅎ𝑦𝜑 | |
2 | nfv 1916 | . 2 ⊢ Ⅎ𝑥𝜓 | |
3 | cbvreuvwOLD.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
4 | 1, 2, 3 | cbvreuw 3405 | 1 ⊢ (∃!𝑥 ∈ 𝐴 𝜑 ↔ ∃!𝑦 ∈ 𝐴 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∃!wreu 3373 |
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 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-11 2153 ax-12 2170 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-tru 1543 df-ex 1781 df-nf 1785 df-mo 2533 df-eu 2562 df-clel 2809 df-nfc 2884 df-ral 3061 df-rex 3070 df-rmo 3375 df-reu 3376 |
This theorem is referenced by: (None) |
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