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Metamath Proof Explorer

Theorem ax13dgen3

Description: Degenerate instance of ax-13 where bundled variables y and z have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017)

Ref Expression
Assertion ax13dgen3 ⊢ ¬ x = y → y = y → ∀ x y = y

Proof

Step Hyp Ref Expression
1 equid ⊢ y = y
2 1 ax-gen ⊢ ∀ x y = y
3 2 2a1i ⊢ ¬ x = y → y = y → ∀ x y = y