Theorem falimtru 1564

Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) An alternate proof is possible using falim 1556 instead of trud 1549 but the present proof using trud 1549 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 1549	. 2 ⊢ (⊥ → ⊤)
2	1	bitru 1548	1 ⊢ ((⊥ → ⊤) ↔ ⊤)

Syntax hints:   → wi 4   ↔ wb 205  ⊤wtru 1540  ⊥wfal 1551

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 1542

This theorem is referenced by: (None)