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Theorem dvelimALT 1883
Description: Version of dvelim 1890 that doesn't use ax-10 1393. Because it has different distinct variable constraints than dvelim 1890 and is used in important proofs, it would be better if it had a name which does not end in ALT (ideally more close to set.mm naming). (Contributed by NM, 17-May-2008.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
dvelimALT.1
dvelimALT.2
Assertion
Ref Expression
dvelimALT
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,,)   (,)

Proof of Theorem dvelimALT
StepHypRef Expression
1 nfv 1418 . . . 4  F/
2 ax-i12 1395 . . . . . . . . 9
3 orcom 646 . . . . . . . . . 10
43orbi2i 678 . . . . . . . . 9
52, 4mpbi 133 . . . . . . . 8
6 orass 683 . . . . . . . 8
75, 6mpbir 134 . . . . . . 7
8 nfa1 1431 . . . . . . . . . . 11  F/
9 ax16ALT 1736 . . . . . . . . . . 11
108, 9nfd 1413 . . . . . . . . . 10  F/
11 dvelimALT.1 . . . . . . . . . . . 12
1211nfi 1348 . . . . . . . . . . 11  F/
1312a1i 9 . . . . . . . . . 10  F/
1410, 13nfimd 1474 . . . . . . . . 9  F/
15 df-nf 1347 . . . . . . . . . 10  F/
16 id 19 . . . . . . . . . . 11  F/  F/
1712a1i 9 . . . . . . . . . . 11  F/  F/
1816, 17nfimd 1474 . . . . . . . . . 10  F/  F/
1915, 18sylbir 125 . . . . . . . . 9  F/
2014, 19jaoi 635 . . . . . . . 8  F/
2120orim1i 676 . . . . . . 7  F/
227, 21ax-mp 7 . . . . . 6  F/
23 orcom 646 . . . . . 6  F/  F/
2422, 23mpbi 133 . . . . 5  F/
2524ori 641 . . . 4  F/
261, 25nfald 1640 . . 3  F/
27 ax-17 1416 . . . . 5
28 dvelimALT.2 . . . . 5
2927, 28equsalh 1611 . . . 4
3029nfbii 1359 . . 3  F/  F/
3126, 30sylib 127 . 2  F/
3231nfrd 1410 1
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wb 98   wo 628  wal 1240   F/wnf 1346
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-i12 1395  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643
This theorem is referenced by:  hbsb4  1885
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