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