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Theorem strcoll2 10936
 Description: Version of ax-strcoll 10935 with one DV 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 2550 . . 3
2 rexeq 2551 . . . . . 6
32bibi2d 230 . . . . 5
43albidv 1746 . . . 4
54exbidv 1747 . . 3
61, 5imbi12d 232 . 2
7 ax-strcoll 10935 . . 3
87spi 1470 . 2
96, 8chvarv 1854 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103  wal 1283  wex 1422  wral 2349  wrex 2350 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-strcoll 10935 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355 This theorem is referenced by:  strcollnft  10937  strcollnfALT  10939
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