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Mirrors > Home > MPE Home > Th. List > ssrab2OLD | Structured version Visualization version GIF version |
Description: Obsolete version of ssrab2 3979 as of 8-Aug-2024. (Contributed by NM, 19-Mar-1997.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
ssrab2OLD | ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} ⊆ 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rab 3060 | . 2 ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} = {𝑥 ∣ (𝑥 ∈ 𝐴 ∧ 𝜑)} | |
2 | ssab2 3978 | . 2 ⊢ {𝑥 ∣ (𝑥 ∈ 𝐴 ∧ 𝜑)} ⊆ 𝐴 | |
3 | 1, 2 | eqsstri 3921 | 1 ⊢ {𝑥 ∈ 𝐴 ∣ 𝜑} ⊆ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 399 ∈ wcel 2112 {cab 2714 {crab 3055 ⊆ wss 3853 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2018 ax-8 2114 ax-9 2122 ax-ext 2708 |
This theorem depends on definitions: df-bi 210 df-an 400 df-tru 1546 df-ex 1788 df-sb 2073 df-clab 2715 df-cleq 2728 df-clel 2809 df-rab 3060 df-v 3400 df-in 3860 df-ss 3870 |
This theorem is referenced by: (None) |
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