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Metamath Proof Explorer

Theorem mpbiran2

Description: Detach truth from conjunction in biconditional. (Contributed by NM, 22-Feb-1996)

Ref Expression
Hypotheses mpbiran2.1 ⊢ χ
mpbiran2.2 ⊢ φ ↔ ψ ∧ χ
Assertion mpbiran2 ⊢ φ ↔ ψ

Proof

Step Hyp Ref Expression
1 mpbiran2.1 ⊢ χ
2 mpbiran2.2 ⊢ φ ↔ ψ ∧ χ
3 2 biancomi ⊢ φ ↔ χ ∧ ψ
4 1 3 mpbiran ⊢ φ ↔ ψ