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Theorem strcollnf 13183
 Description: Version of ax-strcoll 13180 with one disjoint variable condition removed, the other disjoint variable condition replaced with a non-freeness hypothesis, and without initial universal quantifier. (Contributed by BJ, 21-Oct-2019.)
Hypothesis
Ref Expression
strcollnf.nf
Assertion
Ref Expression
strcollnf
Distinct variable group:   ,,,
Allowed substitution hints:   (,,,)

Proof of Theorem strcollnf
StepHypRef Expression
1 strcollnft 13182 . 2
2 strcollnf.nf . . 3
32ax-gen 1425 . 2
41, 3mpg 1427 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1329  wnf 1436  wex 1468  wral 2416  wrex 2417 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 2121  ax-strcoll 13180 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422 This theorem is referenced by: (None)
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