NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  ax12dgen3 GIF version

Theorem ax12dgen3 1727
Description: Degenerate instance of ax-12 1925 where bundled variables y and z have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017.)
Assertion
Ref Expression
ax12dgen3 x = y → (y = yx y = y))

Proof of Theorem ax12dgen3
StepHypRef Expression
1 equid 1676 . . 3 y = y
21ax-gen 1546 . 2 x y = y
322a1i 24 1 x = y → (y = yx y = y))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675
This theorem depends on definitions:  df-bi 177  df-ex 1542
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator