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Mirrors > Home > MPE Home > Th. List > csbieOLD | Structured version Visualization version GIF version |
Description: Obsolete version of csbie 3924 as of 15-Oct-2024. (Contributed by AV, 2-Dec-2019.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
csbieOLD.1 | ⊢ 𝐴 ∈ V |
csbieOLD.2 | ⊢ (𝑥 = 𝐴 → 𝐵 = 𝐶) |
Ref | Expression |
---|---|
csbieOLD | ⊢ ⦋𝐴 / 𝑥⦌𝐵 = 𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbieOLD.1 | . 2 ⊢ 𝐴 ∈ V | |
2 | nfcv 2897 | . 2 ⊢ Ⅎ𝑥𝐶 | |
3 | csbieOLD.2 | . 2 ⊢ (𝑥 = 𝐴 → 𝐵 = 𝐶) | |
4 | 1, 2, 3 | csbief 3923 | 1 ⊢ ⦋𝐴 / 𝑥⦌𝐵 = 𝐶 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1533 ∈ wcel 2098 Vcvv 3468 ⦋csb 3888 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2163 ax-ext 2697 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-3an 1086 df-tru 1536 df-ex 1774 df-nf 1778 df-sb 2060 df-clab 2704 df-cleq 2718 df-clel 2804 df-nfc 2879 df-v 3470 df-sbc 3773 df-csb 3889 |
This theorem is referenced by: (None) |
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