Theorem falimtru 1679

Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) An alternate proof is possible using falim 1671 instead of trud 1664 but the present proof using trud 1664 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 1664	. 2 ⊢ (⊥ → ⊤)
2	1	bitru 1663	1 ⊢ ((⊥ → ⊤) ↔ ⊤)

Syntax hints:   → wi 4   ↔ wb 198  ⊤wtru 1654  ⊥wfal 1666

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 199  df-tru 1657

This theorem is referenced by: (None)