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Mirrors > Home > MPE Home > Th. List > Mathboxes > el3v2 | 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, 16-Oct-2020.) |
Ref | Expression |
---|---|
el3v2.1 | ⊢ ((𝜑 ∧ 𝑦 ∈ V ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
el3v2 | ⊢ ((𝜑 ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3203 | . 2 ⊢ 𝑦 ∈ V | |
2 | el3v2.1 | . 2 ⊢ ((𝜑 ∧ 𝑦 ∈ V ∧ 𝜒) → 𝜃) | |
3 | 1, 2 | mp3an2 1412 | 1 ⊢ ((𝜑 ∧ 𝜒) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 384 ∧ 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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