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Mirrors > Home > MPE Home > Th. List > nfe1 | Structured version Visualization version GIF version |
Description: The setvar 𝑥 is not free in ∃𝑥𝜑. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfe1 | ⊢ Ⅎ𝑥∃𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbe1 2140 | . 2 ⊢ (∃𝑥𝜑 → ∀𝑥∃𝑥𝜑) | |
2 | 1 | nf5i 2143 | 1 ⊢ Ⅎ𝑥∃𝑥𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ∃wex 1775 Ⅎwnf 1779 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-10 2138 |
This theorem depends on definitions: df-bi 207 df-ex 1776 df-nf 1780 |
This theorem is referenced by: nfa1 2148 nfnf1 2151 sbalex 2239 nf6 2281 exdistrf 2449 nfeu1ALT 2586 euor2 2610 2moexv 2624 moexexvw 2625 2moswapv 2626 2euexv 2628 eupicka 2631 mopick2 2634 moexex 2635 2moex 2637 2euex 2638 2moswap 2641 2mo 2645 2eu7 2655 2eu8 2656 nfre1 3282 ceqsexg 3652 morex 3727 intab 4982 nfopab1 5217 nfopab2 5218 axrep1 5285 axrep2 5287 axrep3 5288 axrep4OLD 5291 eusv2nf 5400 copsexgw 5500 copsexg 5501 copsex2t 5502 mosubopt 5519 dfid3 5585 dmcoss 5987 imadif 6651 oprabidw 7461 nfoprab1 7493 nfoprab2 7494 nfoprab3 7495 zfcndrep 10651 zfcndpow 10653 zfcndreg 10654 zfcndinf 10655 reclem2pr 11085 ex-natded9.26 30447 brabgaf 32627 bnj607 34908 bnj849 34917 bnj1398 35026 bnj1449 35040 finminlem 36300 exisym1 36406 bj-alexbiex 36681 bj-exexbiex 36682 bj-biexal2 36688 bj-biexex 36691 bj-sbf3 36821 copsex2d 37121 sbexi 38099 ac6s6 38158 e2ebind 44560 e2ebindVD 44909 e2ebindALT 44926 stoweidlem57 46012 ovncvrrp 46519 ich2ex 47392 ichreuopeq 47397 reuopreuprim 47450 pgind 48947 |
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