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| Mirrors > Home > MPE Home > Th. List > exsimpr | Structured version Visualization version GIF version | ||
| Description: Simplification of an existentially quantified conjunction. (Contributed by Rodolfo Medina, 25-Sep-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) |
| Ref | Expression |
|---|---|
| exsimpr | ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | simpr 484 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓) | |
| 2 | 1 | eximi 1835 | 1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∧ wa 395 ∃wex 1779 |
| 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 207 df-an 396 df-ex 1780 |
| This theorem is referenced by: 19.40 1886 elex2 2818 rexex 3076 ceqsexv2dOLD 3534 imassrn 6089 fv3 6924 finacn 10090 dfac4 10162 kmlem2 10192 ac6c5 10522 ac6s3 10527 ac6s5 10531 axnulALT2 35107 bj-finsumval0 37286 mptsnunlem 37339 topdifinffinlem 37348 heiborlem3 37820 ac6s3f 38178 moantr 38365 |
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