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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 2611 | . 2 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝜓 ∧ 𝜑)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ∃*𝑥(𝜓 ∧ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 399 ∃*wmo 2596 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1782 df-mo 2598 |
This theorem is referenced by: euxfr2w 3659 euxfr2 3661 rmoeq 3677 reuxfrd 3687 fvopab6 6778 1stconst 7778 2ndconst 7779 iunmapdisj 9434 axaddf 10556 axmulf 10557 joinval 17607 meetval 17621 reuxfrdf 30262 |
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