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Mirrors > Home > ILE Home > Th. List > jcai | GIF version |
Description: Deduction replacing implication with conjunction. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
jcai.1 | ⊢ (𝜑 → 𝜓) |
jcai.2 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
jcai | ⊢ (𝜑 → (𝜓 ∧ 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | jcai.1 | . 2 ⊢ (𝜑 → 𝜓) | |
2 | jcai.2 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
3 | 1, 2 | mpd 13 | . 2 ⊢ (𝜑 → 𝜒) |
4 | 1, 3 | jca 304 | 1 ⊢ (𝜑 → (𝜓 ∧ 𝜒)) |
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: reu6 2919 f1ocnv2d 6050 nnoddn2prm 12201 |
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