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Metamath Proof Explorer

Theorem pm2.61

Description: Theorem *2.61 of WhiteheadRussell p. 107. Useful for eliminating an antecedent. (Contributed by NM, 4-Jan-1993) (Proof shortened by Wolf Lammen, 22-Sep-2013)

		Ref	Expression
	Assertion	pm2.61	⊢ ( ( 𝜑 → 𝜓 ) → ( ( ¬ 𝜑 → 𝜓 ) → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		pm2.6	⊢ ( ( ¬ 𝜑 → 𝜓 ) → ( ( 𝜑 → 𝜓 ) → 𝜓 ) )
2	1	com12	⊢ ( ( 𝜑 → 𝜓 ) → ( ( ¬ 𝜑 → 𝜓 ) → 𝜓 ) )