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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 3869 | . 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 2105 Vcvv 3477 [wsbc 3790 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-8 2107 |
This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1776 df-sb 2062 df-clab 2712 df-clel 2813 df-sbc 3791 |
This theorem is referenced by: bnj976 34769 bnj91 34853 bnj92 34854 bnj523 34879 bnj539 34883 bnj540 34884 bnj1040 34964 |
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