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Theorem ax9vsep 4145
 Description: Derive a weakened version of ax9 1889 ( i.e. ax9v 1636), where and must be distinct, from Separation ax-sep 4141 and Extensionality ax-ext 2264. See ax9 1889 for the derivation of ax9 1889 from ax9v 1636. (Contributed by NM, 12-Nov-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax9vsep
Distinct variable group:   ,

Proof of Theorem ax9vsep
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax-sep 4141 . . 3
2 id 19 . . . . . . . . 9
32biantru 491 . . . . . . . 8
43bibi2i 304 . . . . . . 7
54biimpri 197 . . . . . 6
65alimi 1546 . . . . 5
7 ax-ext 2264 . . . . 5
86, 7syl 15 . . . 4
98eximi 1563 . . 3
101, 9ax-mp 8 . 2
11 df-ex 1529 . 2
1210, 11mpbi 199 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wa 358  wal 1527  wex 1528   wceq 1623   wcel 1684 This theorem is referenced by:  ax9sep  29160 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-ext 2264  ax-sep 4141 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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