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Mirrors > Home > MPE Home > Th. List > Mathboxes > eubiOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of eubi 2628 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 2120 | . 2 ⊢ Ⅎ𝑥∀𝑥(𝜑 ↔ 𝜓) | |
2 | sp 2145 | . 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓)) | |
3 | 1, 2 | eubid 2632 | 1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃!𝑥𝜑 ↔ ∃!𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 207 ∀wal 1520 ∃!weu 2610 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1778 ax-4 1792 ax-5 1889 ax-6 1948 ax-7 1993 ax-10 2111 ax-12 2140 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 843 df-ex 1763 df-nf 1767 df-mo 2575 df-eu 2611 |
This theorem is referenced by: (None) |
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