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Mirrors > Home > MPE Home > Th. List > 3adant2r | Structured version Visualization version GIF version |
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.) |
Ref | Expression |
---|---|
3adant1l.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
3adant2r | ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3adant1l.1 | . . . 4 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
2 | 1 | 3com12 1261 | . . 3 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜒) → 𝜃) |
3 | 2 | 3adant1r 1311 | . 2 ⊢ (((𝜓 ∧ 𝜏) ∧ 𝜑 ∧ 𝜒) → 𝜃) |
4 | 3 | 3com12 1261 | 1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∧ w3a 1031 |
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 196 df-an 385 df-3an 1033 |
This theorem is referenced by: ltdiv23 10793 lediv23 10794 divalglem8 14961 isdrngd 18595 deg1tm 23682 ax5seglem1 25608 ax5seglem2 25609 nvaddsub4 26896 nmoub2i 27013 cdleme21at 34634 cdleme42f 34786 trlcoabs2N 35028 tendoplcl2 35084 tendopltp 35086 cdlemk2 35138 cdlemk8 35144 cdlemk9 35145 cdlemk9bN 35146 cdleml8 35289 dihglblem3N 35602 dihglblem3aN 35603 fourierdlem42 39042 lincscm 42013 |
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