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Theorem disjssi 36999
Description: Subclass theorem for disjoints, inference version. (Contributed by Peter Mazsa, 28-Sep-2021.)
Hypothesis
Ref Expression
disjssi.1 𝐴𝐵
Assertion
Ref Expression
disjssi ( Disj 𝐵 → Disj 𝐴)

Proof of Theorem disjssi
StepHypRef Expression
1 disjssi.1 . 2 𝐴𝐵
2 disjss 36998 . 2 (𝐴𝐵 → ( Disj 𝐵 → Disj 𝐴))
31, 2ax-mp 5 1 ( Disj 𝐵 → Disj 𝐴)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wss 3898   Disj wdisjALTV 36472
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2153  ax-12 2170  ax-ext 2707  ax-sep 5243  ax-nul 5250  ax-pr 5372
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1781  df-nf 1785  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-ral 3062  df-rex 3071  df-rab 3404  df-v 3443  df-dif 3901  df-un 3903  df-in 3905  df-ss 3915  df-nul 4270  df-if 4474  df-sn 4574  df-pr 4576  df-op 4580  df-br 5093  df-opab 5155  df-id 5518  df-xp 5626  df-rel 5627  df-cnv 5628  df-co 5629  df-dm 5630  df-rn 5631  df-res 5632  df-coss 36678  df-cnvrefrel 36794  df-funALTV 36949  df-disjALTV 36972
This theorem is referenced by:  disjimres  37017  disjimin  37018
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