Theorem falimtru 1559

Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) An alternate proof is possible using falim 1551 instead of trud 1544 but the present proof using trud 1544 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 1544	. 2 ⊢ (⊥ → ⊤)
2	1	bitru 1543	1 ⊢ ((⊥ → ⊤) ↔ ⊤)

Syntax hints:   → wi 4   ↔ wb 205  ⊤wtru 1535  ⊥wfal 1546

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 1537

This theorem is referenced by: (None)