MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax9v1 Structured version   Visualization version   GIF version

Theorem ax9v1 1988
Description: First of two weakened versions of ax9v 1987, with an extra dv condition on 𝑥, 𝑧, see comments there. (Contributed by BJ, 7-Dec-2020.)
Ref Expression
ax9v1 (𝑥 = 𝑦 → (𝑧𝑥𝑧𝑦))
Distinct variable groups:   𝑥,𝑦   𝑥,𝑧

Proof of Theorem ax9v1
StepHypRef Expression
1 ax9v 1987 1 (𝑥 = 𝑦 → (𝑧𝑥𝑧𝑦))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-9 1986
This theorem is referenced by:  ax9  1990
  Copyright terms: Public domain W3C validator