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Theorem sspssn 3042
 Description: Like pssn2lp 3039 but for subset and proper subset. (Contributed by Jim Kingdon, 17-Jul-2018.)
Assertion
Ref Expression
sspssn ¬ (AB BA)

Proof of Theorem sspssn
StepHypRef Expression
1 pm3.24 626 . 2 ¬ (BA ¬ BA)
2 ssnpss 3041 . . . 4 (AB → ¬ BA)
32anim2i 324 . . 3 ((BA AB) → (BA ¬ BA))
43ancoms 255 . 2 ((AB BA) → (BA ¬ BA))
51, 4mto 587 1 ¬ (AB BA)
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   ∧ wa 97   ⊆ 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  ax-in1 544  ax-in2 545  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-ne 2203  df-in 2918  df-ss 2925  df-pss 2927 This theorem is referenced by:  sspsstr  3044  psssstr  3045
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