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Theorem strcoll2 13397
 Description: Version of ax-strcoll 13396 with one disjoint variable condition removed and without initial universal quantifier. (Contributed by BJ, 5-Oct-2019.)
Assertion
Ref Expression
strcoll2
Distinct variable groups:   ,,,   ,
Allowed substitution hints:   (,,)

Proof of Theorem strcoll2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 raleq 2631 . . 3
2 raleq 2631 . . . . 5
3 rexeq 2632 . . . . . 6
43ralbidv 2440 . . . . 5
52, 4anbi12d 465 . . . 4
65exbidv 1799 . . 3
71, 6imbi12d 233 . 2
8 ax-strcoll 13396 . . 3
98spi 1517 . 2
107, 9chvarv 1911 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103  wex 1469  wral 2418  wrex 2419 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2123  ax-strcoll 13396 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1738  df-cleq 2134  df-clel 2137  df-nfc 2272  df-ral 2423  df-rex 2424 This theorem is referenced by:  strcollnft  13398  strcollnfALT  13400
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