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Mirrors > Home > MPE Home > Th. List > euanv | Structured version Visualization version GIF version |
Description: Introduction of a conjunct into uniqueness quantifier. (Contributed by NM, 23-Mar-1995.) |
Ref | Expression |
---|---|
euanv | ⊢ (∃!𝑥(𝜑 ∧ 𝜓) ↔ (𝜑 ∧ ∃!𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1992 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | 1 | euan 2668 | 1 ⊢ (∃!𝑥(𝜑 ∧ 𝜓) ↔ (𝜑 ∧ ∃!𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 196 ∧ wa 383 ∃!weu 2607 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1871 ax-4 1886 ax-5 1988 ax-6 2054 ax-7 2090 ax-12 2196 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-ex 1854 df-nf 1859 df-eu 2611 |
This theorem is referenced by: eueq2 3521 2reu5lem1 3554 fsn 6565 dfac5lem5 9140 |
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