Theorem efald2 33047

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 481	. . 3 ⊢ ((⊤ ∧ ¬ 𝜑) → ⊥)
3	2	efald 1495	. 2 ⊢ (⊤ → 𝜑)
4	3	trud 1484	1 ⊢ 𝜑

Syntax hints:  ¬ wn 3   → wi 4  ⊤wtru 1476  ⊥wfal 1480

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 196  df-an 385  df-tru 1478  df-fal 1481

This theorem is referenced by:  mpt2bi123f  33141  mptbi12f  33145  ac6s6  33150