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Mirrors > Home > MPE Home > Th. List > mormo | Structured version Visualization version GIF version |
Description: Unrestricted "at most one" implies restricted "at most one". (Contributed by NM, 16-Jun-2017.) |
Ref | Expression |
---|---|
mormo | ⊢ (∃*𝑥𝜑 → ∃*𝑥 ∈ 𝐴 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | moan 2524 | . 2 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | df-rmo 2920 | . 2 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
3 | 1, 2 | sylibr 224 | 1 ⊢ (∃*𝑥𝜑 → ∃*𝑥 ∈ 𝐴 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 384 ∈ wcel 1990 ∃*wmo 2471 ∃*wrmo 2915 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-ex 1705 df-nf 1710 df-eu 2474 df-mo 2475 df-rmo 2920 |
This theorem is referenced by: reueq 3404 reusv1 4866 reusv1OLD 4867 brdom4 9352 phpreu 33393 |
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