Description: Introduce conjunct to both sides of an implication. (Contributed by NM, 5-Aug-1993)
Ref | Expression | ||
---|---|---|---|
Hypothesis | anim1i.1 | ⊢ ( 𝜑 → 𝜓 ) | |
Assertion | anim1i | ⊢ ( ( 𝜑 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜒 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anim1i.1 | ⊢ ( 𝜑 → 𝜓 ) | |
2 | id | ⊢ ( 𝜒 → 𝜒 ) | |
3 | 1 2 | anim12i | ⊢ ( ( 𝜑 ∧ 𝜒 ) → ( 𝜓 ∧ 𝜒 ) ) |