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Mirrors > Home > MPE Home > Th. List > camestresOLD | Structured version Visualization version GIF version |
Description: Obsolete proof of camestres 2731 as of 27-Sep-2022. (Contributed by David A. Wheeler, 27-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
camestres.maj | ⊢ ∀𝑥(𝜑 → 𝜓) |
camestres.min | ⊢ ∀𝑥(𝜒 → ¬ 𝜓) |
Ref | Expression |
---|---|
camestresOLD | ⊢ ∀𝑥(𝜒 → ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | camestres.min | . . . 4 ⊢ ∀𝑥(𝜒 → ¬ 𝜓) | |
2 | 1 | spi 2218 | . . 3 ⊢ (𝜒 → ¬ 𝜓) |
3 | camestres.maj | . . . 4 ⊢ ∀𝑥(𝜑 → 𝜓) | |
4 | 3 | spi 2218 | . . 3 ⊢ (𝜑 → 𝜓) |
5 | 2, 4 | nsyl 138 | . 2 ⊢ (𝜒 → ¬ 𝜑) |
6 | 5 | ax-gen 1891 | 1 ⊢ ∀𝑥(𝜒 → ¬ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1651 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1891 ax-4 1905 ax-5 2006 ax-6 2072 ax-7 2107 ax-12 2213 |
This theorem depends on definitions: df-bi 199 df-ex 1876 |
This theorem is referenced by: (None) |
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