Theorem disjssi 39199

Description: Subclass theorem for disjoints, inference version. (Contributed by Peter Mazsa, 28-Sep-2021.)

Hypothesis

Ref	Expression
disjssi.1	⊢ 𝐴 ⊆ 𝐵

Assertion

Ref	Expression
disjssi	⊢ ( Disj 𝐵 → Disj 𝐴)

Proof of Theorem disjssi

Step	Hyp	Ref	Expression
1		disjssi.1	. 2 ⊢ 𝐴 ⊆ 𝐵
2		disjss 39198	. 2 ⊢ (𝐴 ⊆ 𝐵 → ( Disj 𝐵 → Disj 𝐴))
3	1, 2	ax-mp 5	1 ⊢ ( Disj 𝐵 → Disj 𝐴)

Syntax hints:   → wi 4   ⊆ wss 3883   Disj wdisjALTV 38586

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-11 2168  ax-ext 2711  ax-sep 5218  ax-pr 5362

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-3an 1094  df-tru 1550  df-fal 1560  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-ral 3054  df-rex 3064  df-rab 3392  df-v 3433  df-dif 3886  df-un 3888  df-in 3890  df-ss 3900  df-nul 4262  df-if 4455  df-sn 4556  df-pr 4558  df-op 4562  df-br 5073  df-opab 5135  df-id 5513  df-xp 5624  df-rel 5625  df-cnv 5626  df-co 5627  df-dm 5628  df-rn 5629  df-res 5630  df-coss 38868  df-cnvrefrel 38974  df-funALTV 39134  df-disjALTV 39157

This theorem is referenced by:  disjimres  39217  disjimin  39218