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Metamath Proof Explorer

Theorem drnf2

Description: Formula-building lemma for use with the Distinctor Reduction Theorem. (Contributed by Mario Carneiro, 4-Oct-2016) (Proof shortened by Wolf Lammen, 5-May-2018) Usage of this theorem is discouraged because it depends on ax-13 . Use nfbidv instead. (New usage is discouraged.)

Ref Expression
Hypothesis dral1.1 ⊢ ∀ x x = y → φ ↔ ψ
Assertion drnf2 ⊢ ∀ x x = y → Ⅎ z φ ↔ Ⅎ z ψ

Proof

Step Hyp Ref Expression
1 dral1.1 ⊢ ∀ x x = y → φ ↔ ψ
2 nfae ⊢ Ⅎ z ∀ x x = y
3 2 1 nfbidf ⊢ ∀ x x = y → Ⅎ z φ ↔ Ⅎ z ψ