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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 4365. (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 4365 | . 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 1539 ∈ wcel 2106 Vcvv 3432 ⦋csb 3832 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-12 2171 ax-ext 2709 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tru 1542 df-ex 1783 df-nf 1787 df-sb 2068 df-clab 2716 df-cleq 2730 df-clel 2816 df-v 3434 df-sbc 3717 df-csb 3833 |
This theorem is referenced by: sbcop 5403 iuninc 30900 f1od2 31056 bnj110 32838 finxpreclem4 35565 brtrclfv2 41335 onfrALTlem4VD 42506 eubrdm 44530 |
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