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Mirrors > Home > MPE Home > Th. List > csbvargi | Structured version Visualization version GIF version |
Description: The proper substitution of a class for a setvar variable results in the class (if the class exists), in inference form of csbvarg 4436. (Contributed by Giovanni Mascellani, 30-May-2019.) |
Ref | Expression |
---|---|
csbvargi.1 | ⊢ 𝐴 ∈ V |
Ref | Expression |
---|---|
csbvargi | ⊢ ⦋𝐴 / 𝑥⦌𝑥 = 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbvargi.1 | . 2 ⊢ 𝐴 ∈ V | |
2 | csbvarg 4436 | . 2 ⊢ (𝐴 ∈ V → ⦋𝐴 / 𝑥⦌𝑥 = 𝐴) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ⦋𝐴 / 𝑥⦌𝑥 = 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1534 ∈ wcel 2099 Vcvv 3462 ⦋csb 3892 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-12 2167 ax-ext 2697 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1537 df-ex 1775 df-nf 1779 df-sb 2061 df-clab 2704 df-cleq 2718 df-clel 2803 df-v 3464 df-sbc 3777 df-csb 3893 |
This theorem is referenced by: sbcop 5495 iuninc 32481 f1od2 32635 bnj110 34703 finxpreclem4 37101 brtrclfv2 43394 onfrALTlem4VD 44562 eubrdm 46651 |
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