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Mirrors > Home > MPE Home > Th. List > Mathboxes > el3v3 | Structured version Visualization version GIF version |
Description: New way (elv 3500, and the theorems beginning with "el2v" or "el3v") to shorten some proofs. (Contributed by Peter Mazsa, 16-Oct-2020.) |
Ref | Expression |
---|---|
el3v3.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝑧 ∈ V) → 𝜃) |
Ref | Expression |
---|---|
el3v3 | ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3498 | . 2 ⊢ 𝑧 ∈ V | |
2 | el3v3.1 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝑧 ∈ V) → 𝜃) | |
3 | 1, 2 | mp3an3 1446 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 398 ∧ w3a 1083 ∈ wcel 2110 Vcvv 3495 |
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 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-3an 1085 df-ex 1777 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-v 3497 |
This theorem is referenced by: el3v13 35490 el3v23 35491 |
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