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Theorem hbsb2e 1666
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 1664 . 2 ([y / x]φx(x = yyφ))
2 sb2 1628 . . 3 (x(x = yyφ) → [y / x]yφ)
32a5i 1413 . 2 (x(x = yyφ) → x[y / x]yφ)
41, 3syl 14 1 ([y / x]φx[y / x]yφ)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1224  wex 1358  [wsb 1623
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-5 1312  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-11 1374  ax-4 1377  ax-i9 1400  ax-ial 1405
This theorem depends on definitions:  df-bi 110  df-sb 1624
This theorem is referenced by: (None)
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