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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 3483, 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 3482 | . 2 ⊢ 𝑥 ∈ V | |
2 | el2v1.1 | . 2 ⊢ ((𝑥 ∈ V ∧ 𝜑) → 𝜓) | |
3 | 1, 2 | mpan 690 | 1 ⊢ (𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 ∈ wcel 2106 Vcvv 3478 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1540 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-v 3480 |
This theorem is referenced by: el3v12 38207 el3v13 38208 exan3 38276 exanres3 38278 ecin0 38334 disjsuc2 38373 eldm1cossres2 38443 brcosscnv 38454 eqvrelqsel 38598 |
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