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 ) )