Theorem ax11dgen 1722

Description: Degenerate instance of ax-11 1746 where bundled variables x and y have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017.)

Assertion

Ref	Expression
ax11dgen	⊢ (x = x → (∀xφ → ∀x(x = x → φ)))

Proof of Theorem ax11dgen

Step	Hyp	Ref	Expression
1		ax-1 6	. . 3 ⊢ (φ → (x = x → φ))
2	1	alimi 1559	. 2 ⊢ (∀xφ → ∀x(x = x → φ))
3	2	a1i 10	1 ⊢ (x = x → (∀xφ → ∀x(x = x → φ)))

This proof depends on syntax axioms:   → wi 4  ∀wal 1540

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-gen 1546  ax-5 1557

This theorem is used by: (None)