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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 1871 | . 2 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜑) | |
2 | exsimpr 1872 | . 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 1782 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 |
This theorem depends on definitions: df-bi 206 df-an 397 df-ex 1783 |
This theorem is referenced by: 19.40-2 1890 19.40b 1891 19.41v 1953 19.41 2228 exdistrf 2447 uniin 4865 copsexgw 5404 copsexg 5405 dmin 5820 imadif 6518 oprabidw 7306 lfuhgr3 33081 bj-19.41al 34840 bj-nnfan 34930 bj-nnfand 34931 bj-19.42t 34955 |
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