Theorem pm13.193

Description: Theorem *13.193 in WhiteheadRussell p. 179. (Contributed by Andrew Salmon, 3-Jun-2011)

	Ref	Expression
Assertion	pm13.193	⊢ ( ( 𝜑 ∧ 𝑥 = 𝑦 ) ↔ ( [ 𝑦 / 𝑥 ] 𝜑 ∧ 𝑥 = 𝑦 ) )

Proof

Step	Hyp	Ref	Expression
1		sbequ12	⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ [ 𝑦 / 𝑥 ] 𝜑 ) )
2	1	pm5.32ri	⊢ ( ( 𝜑 ∧ 𝑥 = 𝑦 ) ↔ ( [ 𝑦 / 𝑥 ] 𝜑 ∧ 𝑥 = 𝑦 ) )