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Mirrors > Home > ILE Home > Th. List > ancrd | GIF version |
Description: Deduction conjoining antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) (Proof shortened by Wolf Lammen, 1-Nov-2012.) |
Ref | Expression |
---|---|
ancrd.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
ancrd | ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancrd.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | idd 21 | . 2 ⊢ (𝜑 → (𝜓 → 𝜓)) | |
3 | 1, 2 | jcad 305 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜓))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia3 107 |
This theorem is referenced by: impac 379 euan 2056 reupick 3365 prel12 3706 ssrnres 4989 funmo 5146 funssres 5173 dffo4 5576 dffo5 5577 fzospliti 9984 rexuz3 10794 qredeq 11813 prmdvdsfz 11855 |
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