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Mirrors > Home > MPE Home > Th. List > nfs1v | Structured version Visualization version GIF version |
Description: The setvar 𝑥 is not free in [𝑦 / 𝑥]𝜑 when 𝑥 and 𝑦 are distinct. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfs1v | ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbs1 2424 | . 2 ⊢ ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑) | |
2 | 1 | nf5i 2011 | 1 ⊢ Ⅎ𝑥[𝑦 / 𝑥]𝜑 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1699 [wsb 1867 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-12 2034 ax-13 2234 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 |
This theorem is referenced by: mo3 2495 eu1 2498 2mo 2539 2eu6 2546 cbvralf 3141 cbvralsv 3158 cbvrexsv 3159 cbvrab 3171 sbhypf 3226 mob2 3353 reu2 3361 reu2eqd 3370 sbcralt 3477 sbcreu 3482 cbvreucsf 3533 cbvrabcsf 3534 sbcel12 3935 sbceqg 3936 csbif 4088 rabasiun 4459 cbvopab1 4655 cbvopab1s 4657 cbvmptf 4676 cbvmpt 4677 opelopabsb 4910 csbopab 4932 csbopabgALT 4933 opeliunxp 5093 ralxpf 5190 cbviota 5773 csbiota 5797 isarep1 5891 cbvriota 6521 csbriota 6523 onminex 6899 tfis 6946 findes 6988 abrexex2g 7036 abrexex2 7040 dfoprab4f 7117 axrepndlem1 9293 axrepndlem2 9294 uzind4s 11624 mo5f 28708 ac6sf2 28810 esumcvg 29475 bj-mo3OLD 32022 wl-lem-moexsb 32529 wl-mo3t 32537 poimirlem26 32605 sbcalf 33087 sbcexf 33088 sbcrexgOLD 36367 sbcel12gOLD 37775 2sb5nd 37797 2sb5ndALT 38190 opeliun2xp 41904 |
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