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Mirrors > Home > NFE Home > Th. List > ancli | GIF version |
Description: Deduction conjoining antecedent to left of consequent. (Contributed by NM, 12-Aug-1993.) |
Ref | Expression |
---|---|
ancli.1 | ⊢ (φ → ψ) |
Ref | Expression |
---|---|
ancli | ⊢ (φ → (φ ∧ ψ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ (φ → φ) | |
2 | ancli.1 | . 2 ⊢ (φ → ψ) | |
3 | 1, 2 | jca 518 | 1 ⊢ (φ → (φ ∧ ψ)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 358 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 177 df-an 360 |
This theorem is referenced by: pm4.45im 545 mo 2226 2mo 2282 barbari 2305 cesaro 2311 camestros 2312 calemos 2322 lecidg 6196 addlec 6208 |
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