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Mirrors > Home > MPE Home > Th. List > nfrmo1 | Structured version Visualization version GIF version |
Description: The setvar 𝑥 is not free in ∃*𝑥 ∈ 𝐴𝜑. (Contributed by NM, 16-Jun-2017.) |
Ref | Expression |
---|---|
nfrmo1 | ⊢ Ⅎ𝑥∃*𝑥 ∈ 𝐴 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rmo 3114 | . 2 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | nfmo1 2616 | . 2 ⊢ Ⅎ𝑥∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑) | |
3 | 1, 2 | nfxfr 1854 | 1 ⊢ Ⅎ𝑥∃*𝑥 ∈ 𝐴 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 399 Ⅎwnf 1785 ∈ wcel 2111 ∃*wmo 2596 ∃*wrmo 3109 |
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 ax-6 1970 ax-7 2015 ax-10 2142 ax-11 2158 ax-12 2175 |
This theorem depends on definitions: df-bi 210 df-or 845 df-ex 1782 df-nf 1786 df-mo 2598 df-rmo 3114 |
This theorem is referenced by: nfdisj1 5009 2reu3 43666 |
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