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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 476 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓) | |
2 | 1 | eximi 1752 | 1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∃wex 1695 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 |
This theorem depends on definitions: df-bi 196 df-an 385 df-ex 1696 |
This theorem is referenced by: 19.40 1785 spsbe 1871 rexex 2985 ceqsexv2d 3216 imassrn 5396 fv3 6116 finacn 8756 dfac4 8828 kmlem2 8856 ac6c5 9187 ac6s3 9192 ac6s5 9196 bj-finsumval0 32324 mptsnunlem 32361 topdifinffinlem 32371 heiborlem3 32782 ac6s3f 33149 |
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