Theorem falimtru 1587

Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) An alternate proof is possible using falim 1579 instead of trud 1572 but the present proof using trud 1572 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 1572	. 2 ⊢ (⊥ → ⊤)
2	1	bitru 1571	1 ⊢ ((⊥ → ⊤) ↔ ⊤)

Syntax hints:   → wi 4   ↔ wb 208  ⊤wtru 1563  ⊥wfal 1574

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 1565

This theorem is referenced by: (None)