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Theorem bj-axun2 7277
Description: axun2 4118 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 7187 . . . 4 BOUNDED z w
21ax-bdex 7185 . . 3 BOUNDED w x z w
3 df-rex 2286 . . . 4 (w x z ww(w x z w))
4 exancom 1477 . . . 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 7190 . 2 BOUNDED w(z w w x)
7 ax-un 4116 . 2 yz(w(z w w x) → z y)
86, 7bdbm1.3ii 7256 1 yz(z yw(z w w x))
Colors of variables: wff set class
Syntax hints:   wa 97  wb 98  wal 1224  wex 1358  wrex 2281
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 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-4 1377  ax-14 1382  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-ext 2000  ax-un 4116  ax-bd0 7179  ax-bdex 7185  ax-bdel 7187  ax-bdsep 7250
This theorem depends on definitions:  df-bi 110  df-nf 1326  df-cleq 2011  df-clel 2014  df-rex 2286
This theorem is referenced by: (None)
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