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Theorem sspssn 3075
Description: Like pssn2lp 3072 but for subset and proper subset. (Contributed by Jim Kingdon, 17-Jul-2018.)
Assertion
Ref Expression
sspssn ¬ (𝐴𝐵𝐵𝐴)

Proof of Theorem sspssn
StepHypRef Expression
1 pm3.24 637 . 2 ¬ (𝐵𝐴 ∧ ¬ 𝐵𝐴)
2 ssnpss 3074 . . . 4 (𝐴𝐵 → ¬ 𝐵𝐴)
32anim2i 328 . . 3 ((𝐵𝐴𝐴𝐵) → (𝐵𝐴 ∧ ¬ 𝐵𝐴))
43ancoms 259 . 2 ((𝐴𝐵𝐵𝐴) → (𝐵𝐴 ∧ ¬ 𝐵𝐴))
51, 4mto 598 1 ¬ (𝐴𝐵𝐵𝐴)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 101  wss 2944  wpss 2945
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-ne 2221  df-in 2951  df-ss 2958  df-pss 2960
This theorem is referenced by:  sspsstr  3077  psssstr  3078
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