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Metamath Proof Explorer

Theorem pm2.21dd

Description: A contradiction implies anything. Deduction from pm2.21 . (Contributed by Mario Carneiro, 9-Feb-2017) (Proof shortened by Wolf Lammen, 22-Jul-2019)

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

Proof

Step	Hyp	Ref	Expression
1		pm2.21dd.1	⊢ ( 𝜑 → 𝜓 )
2		pm2.21dd.2	⊢ ( 𝜑 → ¬ 𝜓 )
3	1 2	pm2.65i	⊢ ¬ 𝜑
4	3	pm2.21i	⊢ ( 𝜑 → 𝜒 )