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Theorem sb4e 1924
Description: One direction of a simplified definition of substitution that unlike sb4 2053 doesn't require a distinctor antecedent. (Contributed by NM, 2-Feb-2007.)
Assertion
Ref Expression
sb4e ([y / x]φx(x = yyφ))

Proof of Theorem sb4e
StepHypRef Expression
1 sb1 1651 . 2 ([y / x]φx(x = y φ))
2 equs5e 1888 . 2 (x(x = y φ) → x(x = yyφ))
31, 2syl 15 1 ([y / x]φx(x = yyφ))
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358  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-11 1746
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-sb 1649
This theorem is referenced by:  hbsb2e  2042
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