Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
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 1560 instead of trud 1553 but the present proof using trud 1553 emphasizes that the result does not require the principle of explosion. (Proof modification is discouraged.) |
Ref | Expression |
---|---|
falimtru | ⊢ ((⊥ → ⊤) ↔ ⊤) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | trud 1553 | . 2 ⊢ (⊥ → ⊤) | |
2 | 1 | bitru 1552 | 1 ⊢ ((⊥ → ⊤) ↔ ⊤) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 209 ⊤wtru 1544 ⊥wfal 1555 |
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 210 df-tru 1546 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |