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Theorem ax6vsep 4577
Description: Derive a weakened version of ax-6 1747 ( i.e. ax6v 1748), where and must be distinct, from Separation ax-sep 4573 and Extensionality ax-ext 2435. See ax6 2003 for the derivation of ax-6 1747 from ax6v 1748. (Contributed by NM, 12-Nov-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax6vsep
Distinct variable group:   ,

Proof of Theorem ax6vsep
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax-sep 4573 . . 3
2 id 22 . . . . . . . . 9
32biantru 505 . . . . . . . 8
43bibi2i 313 . . . . . . 7
54biimpri 206 . . . . . 6
65alimi 1633 . . . . 5
7 ax-ext 2435 . . . . 5
86, 7syl 16 . . . 4
98eximi 1656 . . 3
101, 9ax-mp 5 . 2
11 df-ex 1613 . 2
1210, 11mpbi 208 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-ext 2435  ax-sep 4573
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613
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