Theorem ax17eq 923

Description: Theorem to add distinct quantifier to atomic formula.

Assertion

Ref	Expression
ax17eq	⊢ (x = y → ∀z x = y)

Distinct variable group(s):   x,z   y,z

Proof of Theorem ax17eq

Step	Hyp	Ref	Expression
1		ax-12 802	. 2 ⊢ (¬ ∀z z = x → (¬ ∀z z = y → (x = y → ∀z x = y)))
2		ax-16 922	. 2 ⊢ (∀z z = x → (x = y → ∀z x = y))
3		ax-16 922	. 2 ⊢ (∀z z = y → (x = y → ∀z x = y))
4	1, 2, 3	pm2.61ii 113	1 ⊢ (x = y → ∀z x = y)

Syntax hints:   → wi 2  ∀wal 672   = weq 797

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-12 802  ax-16 922

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