![]() |
Mathbox for Andrew Salmon |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > eubiOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of eubi 2582 as of 7-Oct-2022. (Contributed by Andrew Salmon, 11-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
eubiOLD | ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃!𝑥𝜑 ↔ ∃!𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 2149 | . 2 ⊢ Ⅎ𝑥∀𝑥(𝜑 ↔ 𝜓) | |
2 | sp 2181 | . 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓)) | |
3 | 1, 2 | eubid 2585 | 1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃!𝑥𝜑 ↔ ∃!𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 206 ∀wal 1535 ∃!weu 2566 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-10 2139 ax-12 2175 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-ex 1777 df-nf 1781 df-mo 2538 df-eu 2567 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |