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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-isseti | Structured version Visualization version GIF version |
Description: Remove from isseti 3182 dependency on ax-ext 2590 (and on df-cleq 2603 and df-v 3175). This proof uses only df-clab 2597 and df-clel 2606 on top of first-order logic. It only uses ax-12 2034 among the auxiliary logical axioms. The hypothesis uses 𝑉 instead of V for extra generality. This is indeed more general as long as elex 3185 is not available. Use bj-issetiv 32057 instead when sufficient (in particular when 𝑉 is substituted for V). (Contributed by BJ, 13-Jun-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-isseti.1 | ⊢ 𝐴 ∈ 𝑉 |
Ref | Expression |
---|---|
bj-isseti | ⊢ ∃𝑥 𝑥 = 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-isseti.1 | . 2 ⊢ 𝐴 ∈ 𝑉 | |
2 | bj-elisset 32056 | . 2 ⊢ (𝐴 ∈ 𝑉 → ∃𝑥 𝑥 = 𝐴) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ∃𝑥 𝑥 = 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 ∃wex 1695 ∈ wcel 1977 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-an 385 df-ex 1696 df-sb 1868 df-clab 2597 df-clel 2606 |
This theorem is referenced by: bj-rexcom4b 32066 |
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