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Theorem strcollnf 10497
 Description: Version of ax-strcoll 10494 with one DV condition removed, the other DV condition replaced by 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 10496 . 2
2 strcollnf.nf . . 3
32ax-gen 1354 . 2
41, 3mpg 1356 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 102  wal 1257  wnf 1365  wex 1397  wral 2323  wrex 2324 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-strcoll 10494 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-rex 2329 This theorem is referenced by: (None)
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