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Theorem ax12v2 1952
 Description: It is possible to remove any restriction on in ax12v 1951. Same as Axiom C8 of [Monk2] p. 105. (Contributed by NM, 5-Aug-1993.) Removed dependencies on ax-10 1932 and ax-13 2104. (Revised by Jim Kingdon, 15-Dec-2017.) (Proof shortened by Wolf Lammen, 8-Dec-2019.)
Assertion
Ref Expression
ax12v2
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem ax12v2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 equtrr 1874 . . 3
2 ax12v 1951 . . . 4
31imim1d 77 . . . . 5
43alimdv 1771 . . . 4
52, 4syl9r 73 . . 3
61, 5syld 44 . 2
7 ax6evr 1867 . 2
86, 7exlimiiv 1785 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wal 1450 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-12 1950 This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672 This theorem is referenced by:  sb56  2096  bj-ax12  31311  wl-lem-exsb  31965  wl-lem-moexsb  31967
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