Theorem efald2 38584

Description: A proof by contradiction. (Contributed by Giovanni Mascellani, 15-Sep-2017.)

Hypothesis

Ref	Expression
efald2.1	⊢ (¬ 𝜑 → ⊥)

Assertion

Ref	Expression
efald2	⊢ 𝜑

Proof of Theorem efald2

Step	Hyp	Ref	Expression
1		efald2.1	. . . 4 ⊢ (¬ 𝜑 → ⊥)
2	1	adantl 486	. . 3 ⊢ ((⊤ ∧ ¬ 𝜑) → ⊥)
3	2	efald 1584	. 2 ⊢ (⊤ → 𝜑)
4	3	mptru 1570	1 ⊢ 𝜑

Syntax hints:  ¬ wn 3   → wi 4  ⊤wtru 1564  ⊥wfal 1575

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 210  df-an 401  df-tru 1566  df-fal 1576

This theorem is referenced by:  mpobi123f  38668  mptbi12f  38672  ac6s6  38678