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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 300 | 1 ⊢ (𝜑 → (𝜓 ∧ 𝜑)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 102 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia3 106 |
This theorem is referenced by: bamalip 2069 gencbvex 2665 mosubt 2792 trsuc 4249 eusv2nf 4278 mosubopt 4503 issref 4814 fo00 5289 eqfnov2 5752 hashfzp1 10228 dfgcd2 11277 |
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