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Metamath Proof Explorer

Theorem dral2-o

Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of Megill p. 448 (p. 16 of preprint). Version of dral2 using ax-c11 . (Contributed by NM, 27-Feb-2005) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypothesis dral2-o.1 ⊢ ∀ x x = y → φ ↔ ψ
Assertion dral2-o ⊢ ∀ x x = y → ∀ z φ ↔ ∀ z ψ

Proof

Step Hyp Ref Expression
1 dral2-o.1 ⊢ ∀ x x = y → φ ↔ ψ
2 hbae-o ⊢ ∀ x x = y → ∀ z ∀ x x = y
3 2 1 albidh ⊢ ∀ x x = y → ∀ z φ ↔ ∀ z ψ