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Theorem hbsb2 1714
 Description: Bound-variable hypothesis builder for substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
hbsb2 x x = y → ([y / x]φx[y / x]φ))

Proof of Theorem hbsb2
StepHypRef Expression
1 sb4 1710 . 2 x x = y → ([y / x]φx(x = yφ)))
2 sb2 1647 . . 3 (x(x = yφ) → [y / x]φ)
32a5i 1432 . 2 (x(x = yφ) → x[y / x]φ)
41, 3syl6 29 1 x x = y → ([y / x]φx[y / x]φ))
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1240  [wsb 1642 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-nf 1347  df-sb 1643 This theorem is referenced by: (None)
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