| Mathbox for Jonathan Ben-Naim |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj525 | Structured version Visualization version GIF version | ||
| Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| bnj525.1 | ⊢ 𝐴 ∈ V |
| Ref | Expression |
|---|---|
| bnj525 | ⊢ ([𝐴 / 𝑥]𝜑 ↔ 𝜑) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bnj525.1 | . 2 ⊢ 𝐴 ∈ V | |
| 2 | sbcg 3863 | . 2 ⊢ (𝐴 ∈ V → ([𝐴 / 𝑥]𝜑 ↔ 𝜑)) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ ([𝐴 / 𝑥]𝜑 ↔ 𝜑) |
| Colors of variables: wff setvar class |
| Syntax hints: ↔ wb 206 ∈ wcel 2108 Vcvv 3480 [wsbc 3788 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-sb 2065 df-clab 2715 df-clel 2816 df-sbc 3789 |
| This theorem is referenced by: bnj976 34791 bnj91 34875 bnj92 34876 bnj523 34901 bnj539 34905 bnj540 34906 bnj1040 34986 |
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