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Mirrors > Home > MPE Home > Th. List > adantrlr | Structured version Visualization version GIF version |
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.) |
Ref | Expression |
---|---|
adantr2.1 | ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) |
Ref | Expression |
---|---|
adantrlr | ⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜏) ∧ 𝜒)) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 482 | . 2 ⊢ ((𝜓 ∧ 𝜏) → 𝜓) | |
2 | adantr2.1 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) | |
3 | 1, 2 | sylanr1 682 | 1 ⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜏) ∧ 𝜒)) → 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: smoord 8403 addsrmo 11110 mulsrmo 11111 lediv12a 12158 nrmmetd 24602 pntrmax 27622 ablo4 30578 mdslmd3i 32360 atom1d 32381 fsumiunle 32835 esumiun 34074 poimirlem28 37634 fdc 37731 incsequz 37734 crngm4 37989 ps-2 39460 aacllem 49031 |
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