NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  ax11dgen GIF version

Theorem ax11dgen 1722
Description: Degenerate instance of ax-11 1746 where bundled variables x and y have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017.)
Assertion
Ref Expression
ax11dgen (x = x → (xφx(x = xφ)))

Proof of Theorem ax11dgen
StepHypRef Expression
1 ax-1 6 . . 3 (φ → (x = xφ))
21alimi 1559 . 2 (xφx(x = xφ))
32a1i 10 1 (x = x → (xφx(x = xφ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-gen 1546  ax-5 1557
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator