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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-extru | Structured version Visualization version GIF version |
Description: There exists a variable such that ⊤ holds; that is, there exists a variable. This corresponds under the standard translation to one of the formulations of the modal axiom (D), the other being 19.2 1949. (This is also extt 32528; propose to move to Main extt 32528 and allt 32525; relabel exiftru 1948 to "exgen", for "existential generalization", which is the standard name for that rule of inference ? ). (Contributed by BJ, 12-May-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-extru | ⊢ ∃𝑥⊤ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1527 | . 2 ⊢ ⊤ | |
2 | 1 | exiftru 1948 | 1 ⊢ ∃𝑥⊤ |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1524 ∃wex 1744 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1762 ax-4 1777 ax-6 1945 |
This theorem depends on definitions: df-bi 197 df-tru 1526 df-ex 1745 |
This theorem is referenced by: (None) |
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