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Mirrors > Home > ILE Home > Th. List > exsimpr | 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 109 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓) | |
2 | 1 | eximi 1579 | 1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ∃wex 1468 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: onm 4318 imassrn 4887 fv3 5437 relelfvdm 5446 nfvres 5447 brtpos2 6141 |
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