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Mirrors > Home > ILE Home > Th. List > jctird | GIF version |
Description: Deduction conjoining a theorem to right of consequent in an implication. (Contributed by NM, 21-Apr-2005.) |
Ref | Expression |
---|---|
jctird.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
jctird.2 | ⊢ (𝜑 → 𝜃) |
Ref | Expression |
---|---|
jctird | ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜃))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | jctird.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | jctird.2 | . . 3 ⊢ (𝜑 → 𝜃) | |
3 | 2 | a1d 22 | . 2 ⊢ (𝜑 → (𝜓 → 𝜃)) |
4 | 1, 3 | jcad 307 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜃))) |
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: anc2ri 330 ordunisuc2r 4515 fnun 5324 fco 5383 fiintim 6930 cauappcvgprlemladdru 7657 cauappcvgprlemladdrl 7658 caucvgprlemnkj 7667 dvdsdivcl 11858 cnrest2 13821 cnptopresti 13823 bdxmet 14086 lgsdir 14521 |
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