This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem ancrd

Description: Deduction conjoining antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994) (Proof shortened by Wolf Lammen, 1-Nov-2012)

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

Proof

Step	Hyp	Ref	Expression
1		ancrd.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		idd	⊢ ( 𝜑 → ( 𝜓 → 𝜓 ) )
3	1 2	jcad	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 ∧ 𝜓 ) ) )