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Metamath Proof Explorer

Theorem sbcid

Description: An identity theorem for substitution. See sbid . (Contributed by Mario Carneiro, 18-Feb-2017)

Ref Expression
Assertion sbcid ⊢ [˙x / x]˙ φ ↔ φ

Proof

Step Hyp Ref Expression
1 sbsbc ⊢ x x φ ↔ [˙x / x]˙ φ
2 sbid ⊢ x x φ ↔ φ
3 1 2 bitr3i ⊢ [˙x / x]˙ φ ↔ φ