Theorem axc5sp1

Description: A special case of ax-c5 without using ax-c5 or ax-5 . (Contributed by NM, 13-Jan-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	axc5sp1	⊢ ( ∀ 𝑦 ¬ 𝑥 = 𝑥 → ¬ 𝑥 = 𝑥 )

Proof

Step	Hyp	Ref	Expression
1		equidqe	⊢ ¬ ∀ 𝑦 ¬ 𝑥 = 𝑥
2	1	pm2.21i	⊢ ( ∀ 𝑦 ¬ 𝑥 = 𝑥 → ¬ 𝑥 = 𝑥 )