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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, inference form. (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 2551 | . 2 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝜓 ∧ 𝜑)) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ ∃*𝑥(𝜓 ∧ 𝜑) | 
| Colors of variables: wff setvar class | 
| Syntax hints: ∧ wa 395 ∃*wmo 2537 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1779 df-mo 2539 | 
| This theorem is referenced by: euxfr2w 3725 euxfr2 3727 rmoeq 3743 reuxfrd 3753 fvopab6 7049 mpofun 7558 1stconst 8126 2ndconst 8127 pwfir 9356 iunmapdisj 10064 axaddf 11186 axmulf 11187 joinval 18423 meetval 18437 reuxfrdf 32511 | 
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