Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-nfs1 Structured version   Visualization version   GIF version

Theorem bj-nfs1 36774
Description: Shorter proof of nfs1 2490 (three essential steps instead of four). (Contributed by BJ, 2-May-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-nfs1.nf 𝑦𝜑
Assertion
Ref Expression
bj-nfs1 𝑥[𝑦 / 𝑥]𝜑

Proof of Theorem bj-nfs1
StepHypRef Expression
1 bj-nfs1t2 36773 . 2 (∀𝑥𝑦𝜑 → Ⅎ𝑥[𝑦 / 𝑥]𝜑)
2 bj-nfs1.nf . 2 𝑦𝜑
31, 2mpg 1793 1 𝑥[𝑦 / 𝑥]𝜑
Colors of variables: wff setvar class
Syntax hints:  wnf 1779  [wsb 2061
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-10 2138  ax-12 2174  ax-13 2374
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-ex 1776  df-nf 1780  df-sb 2062
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator