Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
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 2154 | . 2 ⊢ Ⅎ𝑥∃𝑥𝜑 | |
2 | 1 | 19.3 2202 | 1 ⊢ (∀𝑥∃𝑥𝜑 ↔ ∃𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 208 ∀wal 1535 ∃wex 1780 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-10 2145 ax-12 2177 |
This theorem depends on definitions: df-bi 209 df-ex 1781 df-nf 1785 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |