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Mirrors > Home > MPE Home > Th. List > barbarilem | Structured version Visualization version GIF version |
Description: Lemma for barbari 2731 and the other Aristotelian syllogisms with existential assumption. (Contributed by BJ, 16-Sep-2022.) |
Ref | Expression |
---|---|
barbarilem.min | ⊢ ∃𝑥𝜑 |
barbarilem.maj | ⊢ ∀𝑥(𝜑 → 𝜓) |
Ref | Expression |
---|---|
barbarilem | ⊢ ∃𝑥(𝜑 ∧ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | barbarilem.maj | . 2 ⊢ ∀𝑥(𝜑 → 𝜓) | |
2 | barbarilem.min | . 2 ⊢ ∃𝑥𝜑 | |
3 | exintr 1893 | . 2 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥(𝜑 ∧ 𝜓))) | |
4 | 1, 2, 3 | mp2 9 | 1 ⊢ ∃𝑥(𝜑 ∧ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 ∀wal 1536 ∃wex 1781 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1782 |
This theorem is referenced by: barbari 2731 cesaro 2740 camestros 2741 calemos 2752 |
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