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Mirrors > Home > MPE Home > Th. List > anc2li | Structured version Visualization version GIF version |
Description: Deduction conjoining antecedent to left of consequent in nested implication. (Contributed by NM, 10-Aug-1994.) (Proof shortened by Wolf Lammen, 7-Dec-2012.) |
Ref | Expression |
---|---|
anc2li.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
anc2li | ⊢ (𝜑 → (𝜓 → (𝜑 ∧ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anc2li.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | id 22 | . 2 ⊢ (𝜑 → 𝜑) | |
3 | 1, 2 | jctild 527 | 1 ⊢ (𝜑 → (𝜓 → (𝜑 ∧ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 397 |
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 206 df-an 398 |
This theorem is referenced by: imdistani 570 pwpw0 4777 sssn 4790 pwsnOLD 4862 wfisgOLD 6312 ordtr2 6365 tfis 7795 oeordi 8538 unblem3 9247 trcl 9672 frinsg 9695 clwlkclwwlkfo 29002 h1datomi 30572 ballotlemfc0 33156 ballotlemfcc 33157 pthisspthorcycl 33786 dfrdg4 34589 bj-sbsb 35355 bj-opelidres 35682 clsk1indlem3 42407 sbiota1 42806 |
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