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Mirrors > Home > MPE Home > Th. List > falimtru | Structured version Visualization version GIF version |
Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) An alternate proof is possible using falim 1551 instead of trud 1544 but the present proof using trud 1544 emphasizes that the result does not require the principle of explosion. (Proof modification is discouraged.) |
Ref | Expression |
---|---|
falimtru | ⊢ ((⊥ → ⊤) ↔ ⊤) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | trud 1544 | . 2 ⊢ (⊥ → ⊤) | |
2 | 1 | bitru 1543 | 1 ⊢ ((⊥ → ⊤) ↔ ⊤) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ⊤wtru 1535 ⊥wfal 1546 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 df-tru 1537 |
This theorem is referenced by: (None) |
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