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Mathbox for Peter Mazsa |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > el3v23 | Structured version Visualization version GIF version |
Description: New way (elv 3418, 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 34544 | . 2 ⊢ ((𝜑 ∧ 𝑦 ∈ V) → 𝜃) |
3 | 2 | elvd 3419 | 1 ⊢ (𝜑 → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1111 ∈ wcel 2164 Vcvv 3414 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1894 ax-4 1908 ax-5 2009 ax-6 2075 ax-7 2112 ax-9 2173 ax-12 2220 ax-ext 2803 |
This theorem depends on definitions: df-bi 199 df-an 387 df-3an 1113 df-tru 1660 df-ex 1879 df-sb 2068 df-clab 2812 df-cleq 2818 df-clel 2821 df-v 3416 |
This theorem is referenced by: brxrn2 34678 |
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