Theorem eldisjssi 39343

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

Hypothesis

Ref	Expression
eldisjssi.1	⊢ 𝐴 ⊆ 𝐵

Assertion

Ref	Expression
eldisjssi	⊢ ( ElDisj 𝐵 → ElDisj 𝐴)

Proof of Theorem eldisjssi

Step	Hyp	Ref	Expression
1		eldisjssi.1	. 2 ⊢ 𝐴 ⊆ 𝐵
2		eldisjss 39342	. 2 ⊢ (𝐴 ⊆ 𝐵 → ( ElDisj 𝐵 → ElDisj 𝐴))
3	1, 2	ax-mp 5	1 ⊢ ( ElDisj 𝐵 → ElDisj 𝐴)

Syntax hints:   → wi 4   ⊆ wss 3906   ElDisj weldisj 38725

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-5 1932  ax-6 1989  ax-7 2030  ax-8 2146  ax-9 2154  ax-11 2193  ax-ext 2736  ax-sep 5248  ax-pr 5392

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-3an 1101  df-tru 1565  df-fal 1575  df-ex 1802  df-sb 2093  df-clab 2743  df-cleq 2756  df-clel 2839  df-ral 3079  df-rex 3089  df-rab 3417  df-v 3458  df-dif 3909  df-un 3911  df-in 3913  df-ss 3923  df-nul 4288  df-if 4483  df-sn 4585  df-pr 4587  df-op 4591  df-br 5103  df-opab 5165  df-id 5544  df-xp 5655  df-rel 5656  df-cnv 5657  df-co 5658  df-dm 5659  df-rn 5660  df-res 5661  df-coss 39005  df-cnvrefrel 39111  df-funALTV 39271  df-disjALTV 39294  df-eldisj 39296

This theorem is referenced by: (None)