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Mirrors > Home > ILE Home > Th. List > jctild | GIF version |
Description: Deduction conjoining a theorem to left of consequent in an implication. (Contributed by NM, 21-Apr-2005.) |
Ref | Expression |
---|---|
jctild.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
jctild.2 | ⊢ (𝜑 → 𝜃) |
Ref | Expression |
---|---|
jctild | ⊢ (𝜑 → (𝜓 → (𝜃 ∧ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | jctild.2 | . . 3 ⊢ (𝜑 → 𝜃) | |
2 | 1 | a1d 22 | . 2 ⊢ (𝜑 → (𝜓 → 𝜃)) |
3 | jctild.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
4 | 2, 3 | jcad 307 | 1 ⊢ (𝜑 → (𝜓 → (𝜃 ∧ 𝜒))) |
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: anc2li 329 syl6an 1434 poxp 6232 ssenen 6850 aptiprleml 7637 zmulcl 9305 rexuz3 10998 cau3lem 11122 gcdzeq 12022 isprm3 12117 epttop 13560 lmtopcnp 13720 txcnp 13741 |
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