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Mirrors > Home > MPE Home > Th. List > Mathboxes > el3v12 | Structured version Visualization version GIF version |
Description: New way (elv 33983, el2v 33984 theorems and el3v 33987 theorems) 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 33988 | . 2 ⊢ ((𝑦 ∈ V ∧ 𝜒) → 𝜃) |
3 | 2 | el2v1 33985 | 1 ⊢ (𝜒 → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1037 ∈ wcel 1990 Vcvv 3200 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-12 2047 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-v 3202 |
This theorem is referenced by: (None) |
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