Mathbox for Peter Mazsa |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > el2v1 | Structured version Visualization version GIF version |
Description: New way (elv 3435, 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 3433 | . 2 ⊢ 𝑥 ∈ V | |
2 | el2v1.1 | . 2 ⊢ ((𝑥 ∈ V ∧ 𝜑) → 𝜓) | |
3 | 1, 2 | mpan 687 | 1 ⊢ (𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 ∈ wcel 2106 Vcvv 3429 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2709 |
This theorem depends on definitions: df-bi 206 df-an 397 df-tru 1542 df-ex 1783 df-sb 2068 df-clab 2716 df-cleq 2730 df-clel 2816 df-v 3431 |
This theorem is referenced by: el3v12 36383 el3v13 36384 exan3 36437 exanres3 36439 ecin0 36492 eldm1cossres2 36587 brcosscnv 36598 eqvrelqsel 36737 |
Copyright terms: Public domain | W3C validator |