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Mirrors > Home > MPE Home > Th. List > exsimpl | 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 |
---|---|
exsimpl | ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 474 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑) | |
2 | 1 | eximi 1911 | 1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∃wex 1853 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1871 ax-4 1886 |
This theorem depends on definitions: df-bi 197 df-an 385 df-ex 1854 |
This theorem is referenced by: 19.40 1946 euexALT 2649 moexex 2679 elex 3352 sbc5 3601 r19.2zb 4205 dmcoss 5540 suppimacnvss 7474 unblem2 8380 kmlem8 9191 isssc 16701 bnj1143 31189 bnj1371 31425 bnj1374 31427 bj-elissetv 33183 atex 35213 rtrclex 38444 clcnvlem 38450 pm10.55 39088 |
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