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Theorem sb4 2053
 Description: One direction of a simplified definition of substitution when variables are distinct. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sb4 x x = y → ([y / x]φx(x = yφ)))

Proof of Theorem sb4
StepHypRef Expression
1 sb1 1651 . 2 ([y / x]φx(x = y φ))
2 equs5 1996 . 2 x x = y → (x(x = y φ) → x(x = yφ)))
31, 2syl5 28 1 x x = y → ([y / x]φx(x = yφ)))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 358  ∀wal 1540  ∃wex 1541  [wsb 1648 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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:  sb4b  2054  dfsb2  2055  hbsb2  2057  sbn  2062  sbi1  2063  sbal1  2126
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