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Metamath Proof Explorer

Theorem sbim

Description: Implication inside and outside of a substitution are equivalent. (Contributed by NM, 14-May-1993)

Ref Expression
Assertion sbim ⊢ y x φ → ψ ↔ y x φ → y x ψ

Proof

Step Hyp Ref Expression
1 sbi1 ⊢ y x φ → ψ → y x φ → y x ψ
2 sbi2 ⊢ y x φ → y x ψ → y x φ → ψ
3 1 2 impbii ⊢ y x φ → ψ ↔ y x φ → y x ψ