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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 566 | 1 ⊢ (𝜑 → (𝜓 → (𝜑 ∧ 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 384 |
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 197 df-an 386 |
This theorem is referenced by: imdistani 726 pwpw0 4344 sssn 4358 pwsnALT 4429 wfisg 5715 ordtr2 5768 tfis 7054 oeordi 7667 unblem3 8214 trcl 8604 h1datomi 28440 ballotlemfc0 30554 ballotlemfcc 30555 frinsg 31742 dfrdg4 32058 bj-sbsb 32824 clsk1indlem3 38341 sbiota1 38635 |
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