Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-ax6elem2 Structured version   Visualization version   GIF version

Theorem bj-ax6elem2 33897
Description: Lemma for bj-ax6e 33898. (Contributed by BJ, 22-Dec-2020.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-ax6elem2 (∀𝑥 𝑦 = 𝑧 → ∃𝑥 𝑥 = 𝑦)
Distinct variable group:   𝑥,𝑧

Proof of Theorem bj-ax6elem2
StepHypRef Expression
1 ax6ev 1963 . . 3 𝑥 𝑥 = 𝑧
2 equeucl 2022 . . 3 (𝑥 = 𝑧 → (𝑦 = 𝑧𝑥 = 𝑦))
31, 2eximii 1828 . 2 𝑥(𝑦 = 𝑧𝑥 = 𝑦)
4319.35i 1870 1 (∀𝑥 𝑦 = 𝑧 → ∃𝑥 𝑥 = 𝑦)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1526  wex 1771
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772
This theorem is referenced by:  bj-ax6e  33898
  Copyright terms: Public domain W3C validator