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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 3927 | . 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 2106 Vcvv 3478 ⦋csb 3908 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1540 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-v 3480 df-sbc 3792 df-csb 3909 |
This theorem is referenced by: sbcop 5500 sbccom2lem 38111 |
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