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Theorem equs3 1644
Description: Lemma used in proofs of substitution properties. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
equs3 (x(x = y φ) ↔ ¬ x(x = y → ¬ φ))

Proof of Theorem equs3
StepHypRef Expression
1 alinexa 1578 . 2 (x(x = y → ¬ φ) ↔ ¬ x(x = y φ))
21con2bii 322 1 (x(x = y φ) ↔ ¬ x(x = y → ¬ φ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 176   wa 358  wal 1540  wex 1541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542
This theorem is referenced by:  equs5e  1888  sbn  2062
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