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Theorem exiftru 1750
Description: A companion rule to ax-gen, valid only if an individual exists. Unlike ax-6 1747, it does not require equality on its interface. Some fundamental theorems of predicate logic can be proven from ax-gen 1618, ax-4 1631 and this theorem alone, not requiring ax-7 1790 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 1749 . 2
2 exiftru.1 . . 3
32a1i 11 . 2
41, 3eximii 1658 1
Colors of variables: wff setvar class
Syntax hints:  E.wex 1612
This theorem is referenced by:  19.2  1751  ac6s6  30580
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-6 1747
This theorem depends on definitions:  df-bi 185  df-ex 1613
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