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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 2541 | . 2 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | df-rmo 3365 | . 2 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
3 | 1, 2 | sylibr 233 | 1 ⊢ (∃*𝑥𝜑 → ∃*𝑥 ∈ 𝐴 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 394 ∈ wcel 2099 ∃*wmo 2527 ∃*wrmo 3364 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 |
This theorem depends on definitions: df-bi 206 df-an 395 df-ex 1775 df-mo 2529 df-rmo 3365 |
This theorem is referenced by: reueq 3731 reusv1 5392 brdom4 10562 phpreu 37316 |
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