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Theorem pssdif 3692
Description: A proper subclass has a nonempty difference. (Contributed by Mario Carneiro, 27-Apr-2016.)
Assertion
Ref Expression
pssdif  |-  ( A 
C.  B  ->  ( B  \  A )  =/=  (/) )

Proof of Theorem pssdif
StepHypRef Expression
1 df-pss 3338 . 2  |-  ( A 
C.  B  <->  ( A  C_  B  /\  A  =/= 
B ) )
2 pssdifn0 3691 . 2  |-  ( ( A  C_  B  /\  A  =/=  B )  -> 
( B  \  A
)  =/=  (/) )
31, 2sylbi 189 1  |-  ( A 
C.  B  ->  ( B  \  A )  =/=  (/) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 360    =/= wne 2601    \ cdif 3319    C_ wss 3322    C. wpss 3323   (/)c0 3630
This theorem is referenced by:  pssnel  3695  pgpfac1lem5  15642  fundmpss  25395  dfon2lem6  25420
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-v 2960  df-dif 3325  df-in 3329  df-ss 3336  df-pss 3338  df-nul 3631
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