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Mirrors > Home > MPE Home > Th. List > pssned | Structured version Visualization version GIF version |
Description: Proper subclasses are unequal. Deduction form of pssne 4109. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
pssssd.1 | ⊢ (𝜑 → 𝐴 ⊊ 𝐵) |
Ref | Expression |
---|---|
pssned | ⊢ (𝜑 → 𝐴 ≠ 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pssssd.1 | . 2 ⊢ (𝜑 → 𝐴 ⊊ 𝐵) | |
2 | pssne 4109 | . 2 ⊢ (𝐴 ⊊ 𝐵 → 𝐴 ≠ 𝐵) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝐴 ≠ 𝐵) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ≠ wne 2938 ⊊ wpss 3964 |
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 207 df-an 396 df-pss 3983 |
This theorem is referenced by: omsucne 7906 ackbij1lem15 10271 canthnumlem 10686 canthp1lem2 10691 mrieqv2d 17684 slwpss 19645 topdifinffinlem 37330 lsatssn0 38984 islshpcv 39035 lkrpssN 39145 |
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