Description: Replace ax-10 in nfa1 with a substitution hypothesis. (Contributed by SN, 2-Sep-2025)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | nfa1w.x | ⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) ) | |
| Assertion | nfa1w | ⊢ Ⅎ 𝑥 ∀ 𝑥 𝜑 | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | nfa1w.x | ⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) ) | |
| 2 | 1 | cbvalvw | ⊢ ( ∀ 𝑥 𝜑 ↔ ∀ 𝑦 𝜓 ) | 
| 3 | nfv | ⊢ Ⅎ 𝑥 ∀ 𝑦 𝜓 | |
| 4 | 2 3 | nfxfr | ⊢ Ⅎ 𝑥 ∀ 𝑥 𝜑 |