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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-alexbiex | Structured version Visualization version GIF version |
Description: Adding a second quantifier is a tranparent operation, (∀∃ case). (Contributed by BJ, 20-Oct-2019.) |
Ref | Expression |
---|---|
bj-alexbiex | ⊢ (∀𝑥∃𝑥𝜑 ↔ ∃𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfe1 2150 | . 2 ⊢ Ⅎ𝑥∃𝑥𝜑 | |
2 | 1 | 19.3 2198 | 1 ⊢ (∀𝑥∃𝑥𝜑 ↔ ∃𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 208 ∀wal 1531 ∃wex 1776 |
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 1907 ax-6 1966 ax-7 2011 ax-10 2141 ax-12 2173 |
This theorem depends on definitions: df-bi 209 df-ex 1777 df-nf 1781 |
This theorem is referenced by: (None) |
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