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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 3148 | . 2 ⊢ (∃*𝑥 ∈ 𝐴 𝜑 ↔ ∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑)) | |
2 | nfmo1 2641 | . 2 ⊢ Ⅎ𝑥∃*𝑥(𝑥 ∈ 𝐴 ∧ 𝜑) | |
3 | 1, 2 | nfxfr 1853 | 1 ⊢ Ⅎ𝑥∃*𝑥 ∈ 𝐴 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 398 Ⅎwnf 1784 ∈ wcel 2114 ∃*wmo 2620 ∃*wrmo 3143 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-10 2145 ax-11 2161 ax-12 2177 |
This theorem depends on definitions: df-bi 209 df-or 844 df-ex 1781 df-nf 1785 df-mo 2622 df-rmo 3148 |
This theorem is referenced by: nfdisj1 5047 2reu3 43316 |
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