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Mirrors > Home > ILE Home > Th. List > moani | 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 2095 | . 2 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝜓 ∧ 𝜑)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ∃*𝑥(𝜓 ∧ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ∧ wa 104 ∃*wmo 2027 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 |
This theorem is referenced by: euxfr2dc 2922 fvopab6 5612 1stconst 6221 2ndconst 6222 axaddf 7866 axmulf 7867 |
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