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Mirrors > Home > ILE 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 306 | 1 ⊢ (𝜑 → (𝜓 ∧ 𝜑)) |
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: bamalip 2159 gencbvex 2798 mosubt 2929 trsuc 4440 eusv2nf 4474 mosubopt 4709 issref 5029 fo00 5516 eqfnov2 6005 hashfzp1 10839 dfgcd2 12050 |
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