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Mathbox for Peter Mazsa |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > el3v12 | Structured version Visualization version GIF version |
Description: New way (elv 3449, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 11-Jul-2021.) |
Ref | Expression |
---|---|
el3v12.1 | ⊢ ((𝑥 ∈ V ∧ 𝑦 ∈ V ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
el3v12 | ⊢ (𝜒 → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | el3v12.1 | . . 3 ⊢ ((𝑥 ∈ V ∧ 𝑦 ∈ V ∧ 𝜒) → 𝜃) | |
2 | 1 | el3v1 36610 | . 2 ⊢ ((𝑦 ∈ V ∧ 𝜒) → 𝜃) |
3 | 2 | el2v1 36608 | 1 ⊢ (𝜒 → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1087 ∈ wcel 2106 Vcvv 3443 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2707 |
This theorem depends on definitions: df-bi 206 df-an 397 df-3an 1089 df-tru 1544 df-ex 1782 df-sb 2068 df-clab 2714 df-cleq 2728 df-clel 2814 df-v 3445 |
This theorem is referenced by: (None) |
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