Description: Generalization rule on a conjunction. Forward inference associated with 19.26 . (Contributed by BJ, 7-Jul-2021)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | bj-genr.1 | ⊢ ( 𝜑 ∧ 𝜓 ) | |
| Assertion | bj-genan | ⊢ ( ∀ 𝑥 𝜑 ∧ ∀ 𝑥 𝜓 ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bj-genr.1 | ⊢ ( 𝜑 ∧ 𝜓 ) | |
| 2 | 1 | simpli | ⊢ 𝜑 |
| 3 | 2 | ax-gen | ⊢ ∀ 𝑥 𝜑 |
| 4 | 1 | simpri | ⊢ 𝜓 |
| 5 | 4 | ax-gen | ⊢ ∀ 𝑥 𝜓 |
| 6 | 3 5 | pm3.2i | ⊢ ( ∀ 𝑥 𝜑 ∧ ∀ 𝑥 𝜓 ) |