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 ) |