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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 307 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜓))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia3 108 |
This theorem is referenced by: impac 381 euan 2094 reupick 3434 prel12 3786 ssrnres 5089 funmo 5250 funssres 5277 dffo4 5684 dffo5 5685 fzospliti 10205 rexuz3 11030 qredeq 12127 prmdvdsfz 12170 |
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