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Theorem exiftru 1797
 Description: A companion rule to ax-gen, valid only if an individual exists. Unlike ax-6 1794, it does not require equality on its interface. Some fundamental theorems of predicate logic can be proven from ax-gen 1665, ax-4 1678 and this theorem alone, not requiring ax-7 1839 or excessive distinct variable conditions. (Contributed by Wolf Lammen, 12-Nov-2017.) (Proof shortened by Wolf Lammen, 9-Dec-2017.)
Hypothesis
Ref Expression
exiftru.1
Assertion
Ref Expression
exiftru

Proof of Theorem exiftru
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax6ev 1796 . 2
2 exiftru.1 . . 3
32a1i 11 . 2
41, 3eximii 1704 1
 Colors of variables: wff setvar class Syntax hints:  wex 1659 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-6 1794 This theorem depends on definitions:  df-bi 188  df-ex 1660 This theorem is referenced by:  19.2  1798  bj-extru  31216  ac6s6  32329
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