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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 4392. (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 4392 | . 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 1542 ∈ wcel 2107 Vcvv 3444 ⦋csb 3856 |
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 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-12 2172 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-nf 1787 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-v 3446 df-sbc 3741 df-csb 3857 |
This theorem is referenced by: sbcop 5447 iuninc 31525 f1od2 31685 bnj110 33527 finxpreclem4 35911 brtrclfv2 42087 onfrALTlem4VD 43256 eubrdm 45356 |
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