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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 4382. (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 4382 | . 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 1533 ∈ wcel 2110 Vcvv 3494 ⦋csb 3882 |
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 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-12 2173 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-v 3496 df-sbc 3772 df-csb 3883 |
This theorem is referenced by: sbcop 5372 iuninc 30306 f1od2 30451 bnj110 32125 finxpreclem4 34669 brtrclfv2 40065 onfrALTlem4VD 41213 eubrdm 43265 |
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