Theorem efald2

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

	Ref	Expression
Hypothesis	efald2.1	⊢ ( ¬ 𝜑 → ⊥ )
Assertion	efald2	⊢ 𝜑

Proof

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