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Metamath Proof Explorer

Theorem anclb

Description: Conjoin antecedent to left of consequent. Theorem *4.7 of WhiteheadRussell p. 120. (Contributed by NM, 25-Jul-1999) (Proof shortened by Wolf Lammen, 24-Mar-2013)

		Ref	Expression
	Assertion	anclb	⊢ ( ( 𝜑 → 𝜓 ) ↔ ( 𝜑 → ( 𝜑 ∧ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ibar	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜑 ∧ 𝜓 ) ) )
2	1	pm5.74i	⊢ ( ( 𝜑 → 𝜓 ) ↔ ( 𝜑 → ( 𝜑 ∧ 𝜓 ) ) )