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Theorem strcollnfALT 13173
 Description: Alternate proof of strcollnf 13172, not using strcollnft 13171. (Contributed by BJ, 5-Oct-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
strcollnf.nf
Assertion
Ref Expression
strcollnfALT
Distinct variable group:   ,,,
Allowed substitution hints:   (,,,)

Proof of Theorem strcollnfALT
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 strcoll2 13170 . 2
2 nfv 1508 . . . . 5
3 nfcv 2279 . . . . . 6
4 strcollnf.nf . . . . . 6
53, 4nfrexxy 2470 . . . . 5
62, 5nfbi 1568 . . . 4
76nfal 1555 . . 3
8 nfv 1508 . . 3
9 elequ2 1691 . . . . 5
109bibi1d 232 . . . 4
1110albidv 1796 . . 3
127, 8, 11cbvex 1729 . 2
131, 12sylib 121 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1329  wnf 1436  wex 1468  wral 2414  wrex 2415 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119  ax-strcoll 13169 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419  df-rex 2420 This theorem is referenced by: (None)
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