![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 477 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓) | |
2 | 1 | eximi 1798 | 1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 387 ∃wex 1743 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1759 ax-4 1773 |
This theorem depends on definitions: df-bi 199 df-an 388 df-ex 1744 |
This theorem is referenced by: 19.40 1850 spsbeOLDOLD 2432 spsbeALT 2517 rexex 3180 ceqsexv2d 3456 imassrn 5778 fv3 6514 finacn 9268 dfac4 9340 kmlem2 9369 ac6c5 9700 ac6s3 9705 ac6s5 9709 bj-finsumval0 34067 mptsnunlem 34098 topdifinffinlem 34107 heiborlem3 34570 ac6s3f 34930 moantr 35099 |
Copyright terms: Public domain | W3C validator |