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Mirrors > Home > ILE Home > Th. List > jctl | GIF version |
Description: Inference conjoining a theorem to the left of a consequent. (Contributed by NM, 31-Dec-1993.) (Proof shortened by Wolf Lammen, 24-Oct-2012.) |
Ref | Expression |
---|---|
jctl.1 | ⊢ 𝜓 |
Ref | Expression |
---|---|
jctl | ⊢ (𝜑 → (𝜓 ∧ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ (𝜑 → 𝜑) | |
2 | jctl.1 | . 2 ⊢ 𝜓 | |
3 | 1, 2 | jctil 295 | 1 ⊢ (𝜑 → (𝜓 ∧ 𝜑)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia3 101 |
This theorem is referenced by: mpanl1 410 mpanlr1 416 reg2exmidlema 4259 relop 4486 nn0n0n1ge2 8311 expge1 9292 |
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