Metamath Proof Explorer


Theorem ancld

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

Ref Expression
Hypothesis ancld.1 ( 𝜑 → ( 𝜓𝜒 ) )
Assertion ancld ( 𝜑 → ( 𝜓 → ( 𝜓𝜒 ) ) )

Proof

Step Hyp Ref Expression
1 ancld.1 ( 𝜑 → ( 𝜓𝜒 ) )
2 idd ( 𝜑 → ( 𝜓𝜓 ) )
3 2 1 jcad ( 𝜑 → ( 𝜓 → ( 𝜓𝜒 ) ) )