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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 310 | 1 ⊢ (𝜑 → (𝜓 ∧ 𝜑)) |
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: mpanl1 431 mpanlr1 437 reg2exmidlema 4495 relop 4738 nn0n0n1ge2 9239 expge1 10465 4dvdseven 11820 ndvdsp1 11835 |
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