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Mirrors > Home > MPE Home > Th. List > 19.29rOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of 19.29r 1790 as 12-Nov-2020. (Contributed by NM, 18-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
19.29rOLD | ⊢ ((∃𝑥𝜑 ∧ ∀𝑥𝜓) → ∃𝑥(𝜑 ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.29 1789 | . . 3 ⊢ ((∀𝑥𝜓 ∧ ∃𝑥𝜑) → ∃𝑥(𝜓 ∧ 𝜑)) | |
2 | 1 | ancoms 468 | . 2 ⊢ ((∃𝑥𝜑 ∧ ∀𝑥𝜓) → ∃𝑥(𝜓 ∧ 𝜑)) |
3 | exancom 1774 | . 2 ⊢ (∃𝑥(𝜑 ∧ 𝜓) ↔ ∃𝑥(𝜓 ∧ 𝜑)) | |
4 | 2, 3 | sylibr 223 | 1 ⊢ ((∃𝑥𝜑 ∧ ∀𝑥𝜓) → ∃𝑥(𝜑 ∧ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∀wal 1473 ∃wex 1695 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 |
This theorem depends on definitions: df-bi 196 df-an 385 df-ex 1696 |
This theorem is referenced by: (None) |
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