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Mirrors > Home > MPE Home > Th. List > csbconstgi | Structured version Visualization version GIF version |
Description: The proper substitution of a class for a variable in another variable does not modify it, in inference form. (Contributed by Giovanni Mascellani, 30-May-2019.) |
Ref | Expression |
---|---|
csbconstgi.1 | ⊢ 𝐴 ∈ V |
Ref | Expression |
---|---|
csbconstgi | ⊢ ⦋𝐴 / 𝑥⦌𝑦 = 𝑦 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbconstgi.1 | . 2 ⊢ 𝐴 ∈ V | |
2 | csbconstg 3904 | . 2 ⊢ (𝐴 ∈ V → ⦋𝐴 / 𝑥⦌𝑦 = 𝑦) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ⦋𝐴 / 𝑥⦌𝑦 = 𝑦 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 ∈ wcel 2114 Vcvv 3496 ⦋csb 3885 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-12 2177 ax-ext 2795 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-sbc 3775 df-csb 3886 |
This theorem is referenced by: sbcop 5382 sbccom2lem 35404 |
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