MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax12dgen Structured version   Visualization version   GIF version

Theorem ax12dgen 2008
Description: Degenerate instance of ax-12 2044 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
ax12dgen (𝑥 = 𝑥 → (∀𝑥𝜑 → ∀𝑥(𝑥 = 𝑥𝜑)))

Proof of Theorem ax12dgen
StepHypRef Expression
1 ala1 1738 . 2 (∀𝑥𝜑 → ∀𝑥(𝑥 = 𝑥𝜑))
21a1i 11 1 (𝑥 = 𝑥 → (∀𝑥𝜑 → ∀𝑥(𝑥 = 𝑥𝜑)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-gen 1719  ax-4 1734
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator