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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 486 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓) | |
2 | 1 | eximi 1838 | 1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 397 ∃wex 1782 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 |
This theorem depends on definitions: df-bi 206 df-an 398 df-ex 1783 |
This theorem is referenced by: 19.40 1890 elex2 2813 rexex 3076 ceqsexv2d 3496 imassrn 6025 fv3 6861 finacn 9991 dfac4 10063 kmlem2 10092 ac6c5 10423 ac6s3 10428 ac6s5 10432 bj-finsumval0 35802 mptsnunlem 35855 topdifinffinlem 35864 heiborlem3 36318 ac6s3f 36676 moantr 36871 |
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