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Theorem strcoll2 9443
 Description: Version of ax-strcoll 9442 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 2499 . . 3
2 rexeq 2500 . . . . . 6
32bibi2d 221 . . . . 5
43albidv 1702 . . . 4
54exbidv 1703 . . 3
61, 5imbi12d 223 . 2
7 ax-strcoll 9442 . . 3
87spi 1426 . 2
96, 8chvarv 1809 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1240  wex 1378  wral 2300  wrex 2301 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-strcoll 9442 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306 This theorem is referenced by:  strcollnft  9444  strcollnfALT  9446
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