NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  hbsb2e GIF version

Theorem hbsb2e 2042
Description: Special case of a bound-variable hypothesis builder for substitution. (Contributed by NM, 2-Feb-2007.)
Assertion
Ref Expression
hbsb2e ([y / x]φx[y / x]yφ)

Proof of Theorem hbsb2e
StepHypRef Expression
1 sb4e 1924 . 2 ([y / x]φx(x = yyφ))
2 sb2 2023 . . 3 (x(x = yyφ) → [y / x]yφ)
32a5i 1789 . 2 (x(x = yyφ) → x[y / x]yφ)
41, 3syl 15 1 ([y / x]φx[y / x]yφ)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1540  wex 1541  [wsb 1648
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator