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Mirrors > Home > NFE Home > Th. List > ancri | GIF version |
Description: Deduction conjoining antecedent to right of consequent. (Contributed by NM, 15-Aug-1994.) |
Ref | Expression |
---|---|
ancri.1 | ⊢ (φ → ψ) |
Ref | Expression |
---|---|
ancri | ⊢ (φ → (ψ ∧ φ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ancri.1 | . 2 ⊢ (φ → ψ) | |
2 | id 19 | . 2 ⊢ (φ → φ) | |
3 | 1, 2 | jca 518 | 1 ⊢ (φ → (ψ ∧ φ)) |
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: truan 1331 bamalip 2324 gencbvex 2901 funmo 5125 fo00 5318 eqfnov2 5590 caovmo 5645 |
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