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Theorem dvelimALT 1946
 Description: Version of dvelim 1953 that doesn't use ax-10 1451. Because it has different distinct variable constraints than dvelim 1953 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 1476 . . . 4
2 ax-i12 1453 . . . . . . . . 9
3 orcom 688 . . . . . . . . . 10
43orbi2i 720 . . . . . . . . 9
52, 4mpbi 144 . . . . . . . 8
6 orass 725 . . . . . . . 8
75, 6mpbir 145 . . . . . . 7
8 nfa1 1489 . . . . . . . . . . 11
9 ax16ALT 1798 . . . . . . . . . . 11
108, 9nfd 1471 . . . . . . . . . 10
11 dvelimALT.1 . . . . . . . . . . . 12
1211nfi 1406 . . . . . . . . . . 11
1312a1i 9 . . . . . . . . . 10
1410, 13nfimd 1532 . . . . . . . . 9
15 df-nf 1405 . . . . . . . . . 10
16 id 19 . . . . . . . . . . 11
1712a1i 9 . . . . . . . . . . 11
1816, 17nfimd 1532 . . . . . . . . . 10
1915, 18sylbir 134 . . . . . . . . 9
2014, 19jaoi 677 . . . . . . . 8
2120orim1i 718 . . . . . . 7
227, 21ax-mp 7 . . . . . 6
23 orcom 688 . . . . . 6
2422, 23mpbi 144 . . . . 5
2524ori 683 . . . 4
261, 25nfald 1701 . . 3
27 ax-17 1474 . . . . 5
28 dvelimALT.2 . . . . 5
2927, 28equsalh 1672 . . . 4
3029nfbii 1417 . . 3
3126, 30sylib 121 . 2
3231nfrd 1468 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 104   wo 670  wal 1297  wnf 1404 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 585  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-11 1452  ax-i12 1453  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483 This theorem depends on definitions:  df-bi 116  df-nf 1405  df-sb 1704 This theorem is referenced by:  hbsb4  1948
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