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Mirrors > Home > MPE Home > Th. List > festinoALT | Structured version Visualization version GIF version |
Description: Alternate proof of festino 2760, shorter but using more axioms. See comment of dariiALT 2752. (Contributed by David A. Wheeler, 27-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
festino.maj | ⊢ ∀𝑥(𝜑 → ¬ 𝜓) |
festino.min | ⊢ ∃𝑥(𝜒 ∧ 𝜓) |
Ref | Expression |
---|---|
festinoALT | ⊢ ∃𝑥(𝜒 ∧ ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | festino.min | . 2 ⊢ ∃𝑥(𝜒 ∧ 𝜓) | |
2 | festino.maj | . . . . 5 ⊢ ∀𝑥(𝜑 → ¬ 𝜓) | |
3 | 2 | spi 2182 | . . . 4 ⊢ (𝜑 → ¬ 𝜓) |
4 | 3 | con2i 141 | . . 3 ⊢ (𝜓 → ¬ 𝜑) |
5 | 4 | anim2i 618 | . 2 ⊢ ((𝜒 ∧ 𝜓) → (𝜒 ∧ ¬ 𝜑)) |
6 | 1, 5 | eximii 1836 | 1 ⊢ ∃𝑥(𝜒 ∧ ¬ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 398 ∀wal 1534 ∃wex 1779 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 ax-12 2176 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1780 |
This theorem is referenced by: (None) |
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