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Metamath Proof Explorer

Theorem pm3.2im

Description: Theorem *3.2 of WhiteheadRussell p. 111, expressed with primitive connectives (see pm3.2 ). (Contributed by NM, 29-Dec-1992) (Proof shortened by Josh Purinton, 29-Dec-2000)

		Ref	Expression
	Assertion	pm3.2im	⊢ ( 𝜑 → ( 𝜓 → ¬ ( 𝜑 → ¬ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm2.27	⊢ ( 𝜑 → ( ( 𝜑 → ¬ 𝜓 ) → ¬ 𝜓 ) )
2	1	con2d	⊢ ( 𝜑 → ( 𝜓 → ¬ ( 𝜑 → ¬ 𝜓 ) ) )