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Mirrors > Home > MPE Home > Th. List > moani | Structured version Visualization version GIF version |
Description: "At most one" is still true when a conjunct is added. (Contributed by NM, 9-Mar-1995.) |
Ref | Expression |
---|---|
moani.1 | ⊢ ∃*𝑥𝜑 |
Ref | Expression |
---|---|
moani | ⊢ ∃*𝑥(𝜓 ∧ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | moani.1 | . 2 ⊢ ∃*𝑥𝜑 | |
2 | moan 2635 | . 2 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝜓 ∧ 𝜑)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ∃*𝑥(𝜓 ∧ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 398 ∃*wmo 2619 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1780 df-mo 2621 |
This theorem is referenced by: euxfr2w 3714 euxfr2 3716 rmoeq 3732 reuxfrd 3742 fvopab6 6804 1stconst 7798 2ndconst 7799 iunmapdisj 9452 axaddf 10570 axmulf 10571 joinval 17618 meetval 17632 reuxfrdf 30258 |
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