Metamath Proof Explorer


Theorem pm10.14

Description: Theorem *10.14 in WhiteheadRussell p. 146. (Contributed by Andrew Salmon, 17-Jun-2011)

Ref Expression
Assertion pm10.14 ⊢ ∀ x φ ∧ ∀ x ψ → y x φ ∧ y x ψ

Proof

Step Hyp Ref Expression
1 stdpc4 ⊢ ∀ x φ → y x φ
2 stdpc4 ⊢ ∀ x ψ → y x ψ
3 1 2 anim12i ⊢ ∀ x φ ∧ ∀ x ψ → y x φ ∧ y x ψ