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Metamath Proof Explorer

Theorem anbi1

Description: Introduce a right conjunct to both sides of a logical equivalence. Theorem *4.36 of WhiteheadRussell p. 118. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion anbi1 ⊢ φ ↔ ψ → φ ∧ χ ↔ ψ ∧ χ

Proof

Step Hyp Ref Expression
1 id ⊢ φ ↔ ψ → φ ↔ ψ
2 1 anbi1d ⊢ φ ↔ ψ → φ ∧ χ ↔ ψ ∧ χ