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Theorem dfpss2 3023
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 2927 . 2 (AB ↔ (AB AB))
2 df-ne 2203 . . 3 (AB ↔ ¬ A = B)
32anbi2i 430 . 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 1242  wne 2201  wss 2911  wpss 2912
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 2203  df-pss 2927
This theorem is referenced by:  dfpss3  3024  psstr  3043  sspsstr  3044  psssstr  3045  pssv  3261  disj4im  3270  ssnelpss  3283  onpsssuc  4247  f1imapss  5358
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