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Mirrors > Home > MPE Home > Th. List > nf5ri | Structured version Visualization version GIF version |
Description: Consequence of the definition of not-free. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nf5ri.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
nf5ri | ⊢ (𝜑 → ∀𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nf5ri.1 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | nf5r 2052 | . 2 ⊢ (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝜑 → ∀𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 Ⅎwnf 1699 |
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-12 2034 |
This theorem depends on definitions: df-bi 196 df-ex 1696 df-nf 1701 |
This theorem is referenced by: 19.3 2057 alimd 2068 alrimi 2069 eximd 2072 nexd 2076 albid 2077 exbid 2078 hban 2113 hb3an 2114 hba1 2137 nfal 2139 nfexOLD 2141 hbex 2142 cbv2 2258 equs45f 2338 nfs1 2353 sb6f 2373 hbsb 2429 nfsab 2602 nfcrii 2744 hbra1 2926 ralrimi 2940 bnj1316 30145 bnj1379 30155 bnj1468 30170 bnj958 30264 bnj981 30274 bnj1014 30284 bnj1128 30312 bnj1204 30334 bnj1279 30340 bnj1398 30356 bnj1408 30358 bnj1444 30365 bnj1445 30366 bnj1446 30367 bnj1447 30368 bnj1448 30369 bnj1449 30370 bnj1463 30377 bnj1312 30380 bnj1518 30386 bnj1519 30387 bnj1520 30388 bnj1525 30391 bj-cbv2v 31919 bj-equs45fv 31940 bj-nfcrii 32045 mpt2bi123f 33141 |
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