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Theorem aev 1943
 Description: A "distinctor elimination" lemma with no restrictions on variables in the consequent. (Contributed by NM, 8-Nov-2006.) Remove dependency on ax-11 1842. (Revised by Wolf Lammen, 7-Sep-2018.) Remove dependency on ax-13 1999, inspired by an idea of BJ. (Revised by Wolf Lammen, 30-Nov-2019.)
Assertion
Ref Expression
aev
Distinct variable group:   ,

Proof of Theorem aev
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 aevlem1 1939 . . 3
2 ax6ev 1749 . . . 4
3 ax-7 1790 . . . . 5
43aleximi 1653 . . . 4
52, 4mpi 17 . . 3
6 ax5e 1706 . . 3
71, 5, 63syl 20 . 2
8 axc16g 1940 . 2
97, 8mpd 15 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  A.wal 1393  E.wex 1612 This theorem is referenced by:  ax16nf  1944  axc16gALT  2106  2ax6e  2194  wl-naev  29982  wl-ax11-lem2  30026 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-5 1704  ax-6 1747  ax-7 1790  ax-12 1854 This theorem depends on definitions:  df-bi 185  df-ex 1613
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