Theorem falimtru 1595

Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) An alternate proof is possible using falim 1587 instead of trud 1580 but the present proof using trud 1580 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 1580	. 2 ⊢ (⊥ → ⊤)
2	1	bitru 1579	1 ⊢ ((⊥ → ⊤) ↔ ⊤)

This proof depends on syntax axioms:   → wi 4   ↔ wb 209  ⊤wtru 1571  ⊥wfal 1582

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-tru 1573

This theorem is used by: (None)