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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 2524 | . 2 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝜓 ∧ 𝜑)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ∃*𝑥(𝜓 ∧ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ∧ wa 384 ∃*wmo 2471 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-ex 1705 df-nf 1710 df-eu 2474 df-mo 2475 |
This theorem is referenced by: euxfr2 3391 rmoeq 3405 reuxfr2d 4891 fvopab6 6310 1stconst 7265 2ndconst 7266 iunmapdisj 8846 axaddf 9966 axmulf 9967 joinval 17005 meetval 17019 reuxfr3d 29329 |
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