Theorem axi10 2730

Description: Axiom of Quantifier Substitution (intuitionistic logic axiom ax-10). This is just axc11n 2456 by another name. (Contributed by Jim Kingdon, 31-Dec-2017.) (New usage is discouraged.)

Assertion

Ref	Expression
axi10	⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥)

Proof of Theorem axi10

Step	Hyp	Ref	Expression
1		axc11n 2456	1 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥)

Syntax hints:   → wi 4  ∀wal 1557

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-10 2174  ax-12 2211  ax-13 2402

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1799  df-nf 1803

This theorem is referenced by: (None)