Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | bnj525.1 | ⊢ 𝐴 ∈ V | |
| Assertion | bnj525 | ⊢ ( [ 𝐴 / 𝑥 ] 𝜑 ↔ 𝜑 ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bnj525.1 | ⊢ 𝐴 ∈ V | |
| 2 | sbcg | ⊢ ( 𝐴 ∈ V → ( [ 𝐴 / 𝑥 ] 𝜑 ↔ 𝜑 ) ) | |
| 3 | 1 2 | ax-mp | ⊢ ( [ 𝐴 / 𝑥 ] 𝜑 ↔ 𝜑 ) |