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Theorem nfsb4 2081
 Description: A variable not free remains so after substitution with a distinct variable. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 4-Oct-2016.)
Hypothesis
Ref Expression
nfsb4.1 zφ
Assertion
Ref Expression
nfsb4 z z = y → Ⅎz[y / x]φ)

Proof of Theorem nfsb4
StepHypRef Expression
1 nfsb4t 2080 . 2 (xzφ → (¬ z z = y → Ⅎz[y / x]φ))
2 nfsb4.1 . 2 zφ
31, 2mpg 1548 1 z z = y → Ⅎz[y / x]φ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540  Ⅎwnf 1544  [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:  sbco2  2086  nfsb  2109  sbal1  2126
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