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Mirrors > Home > MPE Home > Th. List > csbieOLD | Structured version Visualization version GIF version |
Description: Obsolete version of csbie 3834 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 3833 | 1 ⊢ ⦋𝐴 / 𝑥⦌𝐵 = 𝐶 |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1543 ∈ wcel 2112 Vcvv 3398 ⦋csb 3798 |
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-10 2143 ax-11 2160 ax-12 2177 ax-ext 2708 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-3an 1091 df-tru 1546 df-ex 1788 df-nf 1792 df-sb 2073 df-clab 2715 df-cleq 2728 df-clel 2809 df-nfc 2879 df-v 3400 df-sbc 3684 df-csb 3799 |
This theorem is referenced by: (None) |
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