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Metamath Proof Explorer

Theorem anc2ri

Description: Deduction conjoining antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994) (Proof shortened by Wolf Lammen, 7-Dec-2012)

		Ref	Expression
	Hypothesis	anc2ri.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	Assertion	anc2ri	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 ∧ 𝜑 ) ) )

Proof

Step	Hyp	Ref	Expression
1		anc2ri.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		id	⊢ ( 𝜑 → 𝜑 )
3	1 2	jctird	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 ∧ 𝜑 ) ) )