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Metamath Proof Explorer

Theorem sbid2v

Description: An identity law for substitution. Used in proof of Theorem 9.7 of Megill p. 449 (p. 16 of the preprint). Usage of this theorem is discouraged because it depends on ax-13 . See sbid2vw for a version with an extra disjoint variable condition requiring fewer axioms. (Contributed by NM, 5-Aug-1993) (New usage is discouraged.)

Ref Expression
Assertion sbid2v ⊢ y x x y φ ↔ φ

Proof

Step Hyp Ref Expression
1 nfv ⊢ Ⅎ x φ
2 1 sbid2 ⊢ y x x y φ ↔ φ