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Mathbox for Glauco Siliprandi |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > reximddv3 | Structured version Visualization version GIF version |
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by Glauco Siliprandi, 5-Feb-2022.) |
Ref | Expression |
---|---|
reximddv3.1 | ⊢ (((𝜑 ∧ 𝑥 ∈ 𝐴) ∧ 𝜓) → 𝜒) |
reximddv3.2 | ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓) |
Ref | Expression |
---|---|
reximddv3 | ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reximddv3.1 | . . 3 ⊢ (((𝜑 ∧ 𝑥 ∈ 𝐴) ∧ 𝜓) → 𝜒) | |
2 | 1 | anasss 470 | . 2 ⊢ ((𝜑 ∧ (𝑥 ∈ 𝐴 ∧ 𝜓)) → 𝜒) |
3 | reximddv3.2 | . 2 ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓) | |
4 | 2, 3 | reximddv 3234 | 1 ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 ∈ wcel 2111 ∃wrex 3107 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1782 df-ral 3111 df-rex 3112 |
This theorem is referenced by: rnmptlb 41880 rnmptbddlem 41881 limclner 42293 climisp 42388 climrescn 42390 liminflbuz2 42457 liminflimsupxrre 42459 climxlim2lem 42487 |
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