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Theorem bj-axun2 9346
Description: axun2 4138 from bounded separation. (Contributed by BJ, 15-Oct-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-axun2 yz(z yw(z w w x))
Distinct variable group:   x,w,y,z

Proof of Theorem bj-axun2
StepHypRef Expression
1 ax-bdel 9256 . . . 4 BOUNDED z w
21ax-bdex 9254 . . 3 BOUNDED w x z w
3 df-rex 2306 . . . 4 (w x z ww(w x z w))
4 exancom 1496 . . . 4 (w(w x z w) ↔ w(z w w x))
53, 4bitri 173 . . 3 (w x z ww(z w w x))
62, 5bd0 9259 . 2 BOUNDED w(z w w x)
7 ax-un 4136 . 2 yz(w(z w w x) → z y)
86, 7bdbm1.3ii 9325 1 yz(z yw(z w w x))
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98  wal 1240  wex 1378  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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019  ax-un 4136  ax-bd0 9248  ax-bdex 9254  ax-bdel 9256  ax-bdsep 9319
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-cleq 2030  df-clel 2033  df-rex 2306
This theorem is referenced by: (None)
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