| Mathbox for Jonathan Ben-Naim |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1262 | Structured version Visualization version GIF version | ||
| Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
| Ref | Expression |
|---|---|
| bnj1262.1 | ⊢ 𝐴 ⊆ 𝐵 |
| bnj1262.2 | ⊢ (𝜑 → 𝐶 = 𝐴) |
| Ref | Expression |
|---|---|
| bnj1262 | ⊢ (𝜑 → 𝐶 ⊆ 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bnj1262.2 | . 2 ⊢ (𝜑 → 𝐶 = 𝐴) | |
| 2 | bnj1262.1 | . 2 ⊢ 𝐴 ⊆ 𝐵 | |
| 3 | 1, 2 | eqsstrdi 4028 | 1 ⊢ (𝜑 → 𝐶 ⊆ 𝐵) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 = wceq 1540 ⊆ wss 3951 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-cleq 2729 df-ss 3968 |
| This theorem is referenced by: bnj229 34898 bnj1128 35004 bnj1145 35007 |
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