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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 1860 | . 2 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜑) | |
2 | exsimpr 1861 | . 2 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓) | |
3 | 1, 2 | jca 512 | 1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → (∃𝑥𝜑 ∧ ∃𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 ∃wex 1771 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 |
This theorem depends on definitions: df-bi 208 df-an 397 df-ex 1772 |
This theorem is referenced by: 19.40-2 1879 19.40b 1880 19.41v 1941 19.41 2227 exdistrf 2461 uniin 4850 copsexgw 5372 copsexg 5373 dmin 5773 imadif 6431 oprabidw 7176 lfuhgr3 32263 bj-19.41al 33889 bj-nnfan 33974 bj-nnfand 33975 bj-19.42t 33999 |
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