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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 103 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓) | |
2 | 1 | eximi 1491 | 1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 ∃wex 1381 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: onm 4138 imassrn 4679 fv3 5197 relelfvdm 5205 nfvres 5206 brtpos2 5866 |
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