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Theorem dfpss2 3354
Description: Alternate definition of proper subclass. (Contributed by NM, 7-Feb-1996.)
Assertion
Ref Expression
dfpss2 (AB ↔ (A B ¬ A = B))

Proof of Theorem dfpss2
StepHypRef Expression
1 df-pss 3261 . 2 (AB ↔ (A B AB))
2 df-ne 2518 . . 3 (AB ↔ ¬ A = B)
32anbi2i 675 . 2 ((A B AB) ↔ (A B ¬ A = B))
41, 3bitri 240 1 (AB ↔ (A B ¬ A = B))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176   wa 358   = wceq 1642  wne 2516   wss 3257  wpss 3258
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-ne 2518  df-pss 3261
This theorem is referenced by:  dfpss3  3355  sspss  3368  psstr  3373  npss  3379  pssv  3590  disj4  3599  ssnelpss  3613  sfinltfin  4535
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