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Mirrors > Home > MPE Home > Th. List > syldbl2 | Structured version Visualization version GIF version |
Description: Stacked hypotheseis implies goal. (Contributed by Stanislas Polu, 9-Mar-2020.) |
Ref | Expression |
---|---|
syldbl2.1 | ⊢ ((𝜑 ∧ 𝜓) → (𝜓 → 𝜃)) |
Ref | Expression |
---|---|
syldbl2 | ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syldbl2.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓) → (𝜓 → 𝜃)) | |
2 | 1 | com12 32 | . 2 ⊢ (𝜓 → ((𝜑 ∧ 𝜓) → 𝜃)) |
3 | 2 | anabsi7 671 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 207 df-an 396 |
This theorem is referenced by: elpredimg 6338 rexdif1en 9197 php 9245 fpwwe2lem4 10672 elfzoextl 13757 rprmdvdspow 33541 rprmdvdsprod 33542 constrmon 33749 aks4d1p3 42060 primrootsunit1 42079 primrootlekpowne0 42087 sticksstones1 42128 sticksstones11 42138 unitscyglem2 42178 uspgrimprop 47811 |
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