Theorem sspssr 3043

Description: Subclass in terms of proper subclass. (Contributed by Jim Kingdon, 16-Jul-2018.)

Assertion

Ref	Expression
sspssr	⊢ ((𝐴 ⊊ 𝐵 ∨ 𝐴 = 𝐵) → 𝐴 ⊆ 𝐵)

Proof of Theorem sspssr

Step	Hyp	Ref	Expression
1		pssss 3039	. 2 ⊢ (𝐴 ⊊ 𝐵 → 𝐴 ⊆ 𝐵)
2		eqimss 2997	. 2 ⊢ (𝐴 = 𝐵 → 𝐴 ⊆ 𝐵)
3	1, 2	jaoi 636	1 ⊢ ((𝐴 ⊊ 𝐵 ∨ 𝐴 = 𝐵) → 𝐴 ⊆ 𝐵)

Syntax hints:   → wi 4   ∨ wo 629   = wceq 1243   ⊆ wss 2917   ⊊ wpss 2918

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931  df-pss 2933

This theorem is referenced by: (None)