Theorem ax13dgen4OLD 2005

Description: Obsolete proof of ax13dgen4 2004 as of 10-Oct-2021. (Contributed by NM, 13-Apr-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
ax13dgen4OLD	⊢ (¬ 𝑥 = 𝑥 → (𝑥 = 𝑥 → ∀𝑥 𝑥 = 𝑥))

Proof of Theorem ax13dgen4OLD

Step	Hyp	Ref	Expression
1		ax13dgen1 2001	1 ⊢ (¬ 𝑥 = 𝑥 → (𝑥 = 𝑥 → ∀𝑥 𝑥 = 𝑥))

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1473

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922

This theorem depends on definitions:  df-bi 196  df-ex 1696

This theorem is referenced by: (None)