Theorem pm13.13b

Description: Theorem *13.13 in WhiteheadRussell p. 178 with different variable substitution. (Contributed by Andrew Salmon, 3-Jun-2011)

	Ref	Expression
Assertion	pm13.13b	⊢ ( ( [ 𝐴 / 𝑥 ] 𝜑 ∧ 𝑥 = 𝐴 ) → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		sbceq1a	⊢ ( 𝑥 = 𝐴 → ( 𝜑 ↔ [ 𝐴 / 𝑥 ] 𝜑 ) )
2	1	biimparc	⊢ ( ( [ 𝐴 / 𝑥 ] 𝜑 ∧ 𝑥 = 𝐴 ) → 𝜑 )