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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