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Mathbox for Peter Mazsa |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > el3v1 | Structured version Visualization version GIF version |
Description: New way (elv 3477, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 16-Oct-2020.) |
Ref | Expression |
---|---|
el3v1.1 | ⊢ ((𝑥 ∈ V ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
el3v1 | ⊢ ((𝜓 ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3475 | . 2 ⊢ 𝑥 ∈ V | |
2 | el3v1.1 | . 2 ⊢ ((𝑥 ∈ V ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
3 | 1, 2 | mp3an1 1445 | 1 ⊢ ((𝜓 ∧ 𝜒) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 ∧ w3a 1085 ∈ wcel 2099 Vcvv 3471 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2699 |
This theorem depends on definitions: df-bi 206 df-an 396 df-3an 1087 df-tru 1537 df-ex 1775 df-sb 2061 df-clab 2706 df-cleq 2720 df-clel 2806 df-v 3473 |
This theorem is referenced by: el3v12 37695 br1cossxrnres 37920 |
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