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Mirrors > Home > MPE Home > Th. List > Mathboxes > el3v23 | Structured version Visualization version GIF version |
Description: New way (elv 3404, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 11-Jul-2021.) |
Ref | Expression |
---|---|
el3v23.1 | ⊢ ((𝜑 ∧ 𝑦 ∈ V ∧ 𝑧 ∈ V) → 𝜃) |
Ref | Expression |
---|---|
el3v23 | ⊢ (𝜑 → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | el3v23.1 | . . 3 ⊢ ((𝜑 ∧ 𝑦 ∈ V ∧ 𝑧 ∈ V) → 𝜃) | |
2 | 1 | el3v3 36060 | . 2 ⊢ ((𝜑 ∧ 𝑦 ∈ V) → 𝜃) |
3 | 2 | elvd 3405 | 1 ⊢ (𝜑 → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1089 ∈ wcel 2112 Vcvv 3398 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2018 ax-8 2114 ax-9 2122 ax-ext 2708 |
This theorem depends on definitions: df-bi 210 df-an 400 df-3an 1091 df-tru 1546 df-ex 1788 df-sb 2073 df-clab 2715 df-cleq 2728 df-clel 2809 df-v 3400 |
This theorem is referenced by: brxrn2 36191 |
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