Theorem pm2.21fal

Description: If a wff and its negation are provable, then falsum is provable. (Contributed by Mario Carneiro, 9-Feb-2017)

	Ref	Expression
Hypotheses	pm2.21fal.1	⊢ ( 𝜑 → 𝜓 )
	pm2.21fal.2	⊢ ( 𝜑 → ¬ 𝜓 )
Assertion	pm2.21fal	⊢ ( 𝜑 → ⊥ )

Proof

Step	Hyp	Ref	Expression
1		pm2.21fal.1	⊢ ( 𝜑 → 𝜓 )
2		pm2.21fal.2	⊢ ( 𝜑 → ¬ 𝜓 )
3	1 2	pm2.21dd	⊢ ( 𝜑 → ⊥ )