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Mirrors > Home > MPE Home > Th. List > 19.40 | Structured version Visualization version GIF version |
Description: Theorem 19.40 of [Margaris] p. 90. (Contributed by NM, 26-May-1993.) |
Ref | Expression |
---|---|
19.40 | ⊢ (∃𝑥(𝜑 ∧ 𝜓) → (∃𝑥𝜑 ∧ ∃𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exsimpl 1875 | . 2 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜑) | |
2 | exsimpr 1876 | . 2 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓) | |
3 | 1, 2 | jca 515 | 1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → (∃𝑥𝜑 ∧ ∃𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 ∃wex 1786 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1787 |
This theorem is referenced by: 19.40-2 1894 19.40b 1895 19.41v 1957 19.41 2237 exdistrf 2448 uniin 4832 copsexgw 5357 copsexg 5358 dmin 5764 imadif 6434 oprabidw 7214 lfuhgr3 32665 bj-19.41al 34496 bj-nnfan 34586 bj-nnfand 34587 bj-19.42t 34611 |
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