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Mirrors > Home > MPE Home > Th. List > eubiiOLD | Structured version Visualization version GIF version |
Description: Obsolete version of eubii 2669 as of 27-Sep-2023. (Contributed by NM, 9-Jul-1994.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
eubii.1 | ⊢ (𝜑 ↔ 𝜓) |
Ref | Expression |
---|---|
eubiiOLD | ⊢ (∃!𝑥𝜑 ↔ ∃!𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eubi 2668 | . 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (∃!𝑥𝜑 ↔ ∃!𝑥𝜓)) | |
2 | eubii.1 | . 2 ⊢ (𝜑 ↔ 𝜓) | |
3 | 1, 2 | mpg 1797 | 1 ⊢ (∃!𝑥𝜑 ↔ ∃!𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 208 ∃!weu 2652 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1780 df-mo 2621 df-eu 2653 |
This theorem is referenced by: (None) |
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