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Mirrors > Home > MPE Home > Th. List > 3anidm13 | Structured version Visualization version GIF version |
Description: Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.) |
Ref | Expression |
---|---|
3anidm13.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜑) → 𝜒) |
Ref | Expression |
---|---|
3anidm13 | ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3anidm13.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜑) → 𝜒) | |
2 | 1 | 3com23 1118 | . 2 ⊢ ((𝜑 ∧ 𝜑 ∧ 𝜓) → 𝜒) |
3 | 2 | 3anidm12 1411 | 1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 ∧ w3a 1079 |
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 208 df-an 397 df-3an 1081 |
This theorem is referenced by: npncan2 10901 ltsubpos 11120 leaddle0 11143 subge02 11144 halfaddsub 11858 avglt1 11863 hashssdif 13761 pythagtriplem4 16144 pythagtriplem14 16153 lsmss2 18722 grpoidinvlem2 28209 hvpncan3 28746 bcm1n 30444 revpfxsfxrev 32259 resubidaddid1 39103 3anidm12p1 41017 3impcombi 41028 |
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