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Mirrors > Home > MPE Home > Th. List > moa1 | Structured version Visualization version GIF version |
Description: If an implication holds for at most one value, then its consequent holds for at most one value. See also ala1 1755 and exa1 1756. (Contributed by NM, 28-Jul-1995.) (Proof shortened by Wolf Lammen, 22-Dec-2018.) (Revised by BJ, 29-Mar-2021.) |
Ref | Expression |
---|---|
moa1 | ⊢ (∃*𝑥(𝜑 → 𝜓) → ∃*𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-1 6 | . 2 ⊢ (𝜓 → (𝜑 → 𝜓)) | |
2 | 1 | moimi 2508 | 1 ⊢ (∃*𝑥(𝜑 → 𝜓) → ∃*𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃*wmo 2459 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-12 2034 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-eu 2462 df-mo 2463 |
This theorem is referenced by: (None) |
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