Theorem falimtru 1562

Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) An alternate proof is possible using falim 1554 instead of trud 1547 but the present proof using trud 1547 emphasizes that the result does not require the principle of explosion. (Proof modification is discouraged.)

Assertion

Ref	Expression
falimtru	⊢ ((⊥ → ⊤) ↔ ⊤)

Proof of Theorem falimtru

Step	Hyp	Ref	Expression
1		trud 1547	. 2 ⊢ (⊥ → ⊤)
2	1	bitru 1546	1 ⊢ ((⊥ → ⊤) ↔ ⊤)

Syntax hints:   → wi 4   ↔ wb 208  ⊤wtru 1538  ⊥wfal 1549

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 209  df-tru 1540

This theorem is referenced by: (None)