Users' Mathboxes Mathbox for Scott Fenton < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  wsuceq3 Structured version   Visualization version   GIF version

Theorem wsuceq3 35798
Description: Equality theorem for well-founded successor. (Contributed by Scott Fenton, 13-Jun-2018.)
Assertion
Ref Expression
wsuceq3 (𝑋 = 𝑌 → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑅, 𝐴, 𝑌))

Proof of Theorem wsuceq3
StepHypRef Expression
1 eqid 2734 . 2 𝑅 = 𝑅
2 eqid 2734 . 2 𝐴 = 𝐴
3 wsuceq123 35795 . 2 ((𝑅 = 𝑅𝐴 = 𝐴𝑋 = 𝑌) → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑅, 𝐴, 𝑌))
41, 2, 3mp3an12 1450 1 (𝑋 = 𝑌 → wsuc(𝑅, 𝐴, 𝑋) = wsuc(𝑅, 𝐴, 𝑌))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1536  wsuccwsuc 35791
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1539  df-fal 1549  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-ral 3059  df-rex 3068  df-rab 3433  df-v 3479  df-dif 3965  df-un 3967  df-in 3969  df-ss 3979  df-nul 4339  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4912  df-br 5148  df-opab 5210  df-xp 5694  df-cnv 5696  df-dm 5698  df-rn 5699  df-res 5700  df-ima 5701  df-pred 6322  df-sup 9479  df-inf 9480  df-wsuc 35793
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator