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Mirrors > Home > MPE Home > Th. List > sseqin2OLD | Structured version Visualization version GIF version |
Description: Obsolete proof of sseqin2 3779 as of 22-Jul-2021. (Contributed by NM, 17-May-1994.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
sseqin2OLD | ⊢ (𝐴 ⊆ 𝐵 ↔ (𝐵 ∩ 𝐴) = 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseqin2 3779 | 1 ⊢ (𝐴 ⊆ 𝐵 ↔ (𝐵 ∩ 𝐴) = 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 195 = wceq 1475 ∩ cin 3539 ⊆ wss 3540 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-v 3175 df-in 3547 df-ss 3554 |
This theorem is referenced by: (None) |
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