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Theorem dfpss2 3006
 Description: Alternate definition of proper subclass. (Contributed by NM, 7-Feb-1996.)
Assertion
Ref Expression
dfpss2 (AB ↔ (AB ¬ A = B))

Proof of Theorem dfpss2
StepHypRef Expression
1 df-pss 2910 . 2 (AB ↔ (AB AB))
2 df-ne 2188 . . 3 (AB ↔ ¬ A = B)
32anbi2i 433 . 2 ((AB AB) ↔ (AB ¬ A = B))
41, 3bitri 173 1 (AB ↔ (AB ¬ A = B))
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   ∧ wa 97   ↔ wb 98   = wceq 1228   ≠ wne 2186   ⊆ wss 2894   ⊊ wpss 2895 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101 This theorem depends on definitions:  df-bi 110  df-ne 2188  df-pss 2910 This theorem is referenced by:  dfpss3  3007  psstr  3026  sspsstr  3027  psssstr  3028  pssv  3244  disj4im  3253  ssnelpss  3266  onpsssuc  4231  f1imapss  5340
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