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Metamath Proof Explorer

Theorem pm2.27

Description: This theorem, sometimes called "Assertion" or "Pon" (for "ponens"), can be thought of as a closed form of modus ponens ax-mp . Theorem *2.27 of WhiteheadRussell p. 104. (Contributed by NM, 15-Jul-1993)

		Ref	Expression
	Assertion	pm2.27	⊢ ( 𝜑 → ( ( 𝜑 → 𝜓 ) → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → 𝜓 ) )
2	1	com12	⊢ ( 𝜑 → ( ( 𝜑 → 𝜓 ) → 𝜓 ) )