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 3761 | . 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 209 ∈ wcel 2112 Vcvv 3398 [wsbc 3683 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2018 ax-8 2114 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1788 df-sb 2073 df-clab 2715 df-clel 2809 df-sbc 3684 |
This theorem is referenced by: bnj976 32424 bnj91 32508 bnj92 32509 bnj523 32534 bnj539 32538 bnj540 32539 bnj1040 32619 |
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