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Mathbox for Peter Mazsa |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > el2v1 | Structured version Visualization version GIF version |
Description: New way (elv 3467, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 23-Oct-2018.) |
Ref | Expression |
---|---|
el2v1.1 | ⊢ ((𝑥 ∈ V ∧ 𝜑) → 𝜓) |
Ref | Expression |
---|---|
el2v1 | ⊢ (𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3465 | . 2 ⊢ 𝑥 ∈ V | |
2 | el2v1.1 | . 2 ⊢ ((𝑥 ∈ V ∧ 𝜑) → 𝜓) | |
3 | 1, 2 | mpan 688 | 1 ⊢ (𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 394 ∈ wcel 2098 Vcvv 3461 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2696 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2703 df-cleq 2717 df-clel 2802 df-v 3463 |
This theorem is referenced by: el3v12 37826 el3v13 37827 exan3 37896 exanres3 37898 ecin0 37954 disjsuc2 37993 eldm1cossres2 38063 brcosscnv 38074 eqvrelqsel 38218 |
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