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Metamath Proof Explorer

Theorem anc2l

Description: Conjoin antecedent to left of consequent in nested implication. (Contributed by NM, 10-Aug-1994) (Proof shortened by Wolf Lammen, 14-Jul-2013)

		Ref	Expression
	Assertion	anc2l	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜑 → ( 𝜓 → ( 𝜑 ∧ 𝜒 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.42	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) ↔ ( 𝜑 → ( 𝜓 → ( 𝜑 ∧ 𝜒 ) ) ) )
2	1	biimpi	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜑 → ( 𝜓 → ( 𝜑 ∧ 𝜒 ) ) ) )