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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 467 | . 2 ⊢ ((𝜑 ∧ (𝑥 ∈ 𝐴 ∧ 𝜓)) → 𝜒) |
3 | reximddv3.2 | . 2 ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓) | |
4 | 2, 3 | reximddv 3272 | 1 ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 ∈ wcel 2105 ∃wrex 3136 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 |
This theorem depends on definitions: df-bi 208 df-an 397 df-ex 1772 df-ral 3140 df-rex 3141 |
This theorem is referenced by: rnmptlb 41390 rnmptbddlem 41391 limclner 41808 climisp 41903 climrescn 41905 liminflbuz2 41972 liminflimsupxrre 41974 climxlim2lem 42002 |
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