Description: Restricted quantifier version of Axiom 4 of Mendelson p. 69. (Contributed by NM, 14-Dec-2005)
Ref | Expression | ||
---|---|---|---|
Assertion | rspsbca | ⊢ ( ( 𝐴 ∈ 𝐵 ∧ ∀ 𝑥 ∈ 𝐵 𝜑 ) → [ 𝐴 / 𝑥 ] 𝜑 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspsbc | ⊢ ( 𝐴 ∈ 𝐵 → ( ∀ 𝑥 ∈ 𝐵 𝜑 → [ 𝐴 / 𝑥 ] 𝜑 ) ) | |
2 | 1 | imp | ⊢ ( ( 𝐴 ∈ 𝐵 ∧ ∀ 𝑥 ∈ 𝐵 𝜑 ) → [ 𝐴 / 𝑥 ] 𝜑 ) |