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Theorem equs5a 1887
Description: A property related to substitution that unlike equs5 1996 doesn't require a distinctor antecedent. (Contributed by NM, 2-Feb-2007.)
Assertion
Ref Expression
equs5a (x(x = y yφ) → x(x = yφ))

Proof of Theorem equs5a
StepHypRef Expression
1 nfa1 1788 . 2 xx(x = yφ)
2 ax-11 1746 . . 3 (x = y → (yφx(x = yφ)))
32imp 418 . 2 ((x = y yφ) → x(x = yφ))
41, 3exlimi 1803 1 (x(x = y yφ) → x(x = yφ))
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358  wal 1540  wex 1541
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-11 1746
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545
This theorem is referenced by:  sb4a  1923  equs45f  1989
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