Theorem frege55lem2b

Description: Lemma for frege55b . Core proof of Proposition 55 of Frege1879 p. 50. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege55lem2b	⊢ ( 𝑥 = 𝑦 → [ 𝑦 / 𝑧 ] 𝑧 = 𝑥 )

Proof

Step	Hyp	Ref	Expression
1		frege54cor1b	⊢ [ 𝑥 / 𝑧 ] 𝑧 = 𝑥
2		frege53b	⊢ ( [ 𝑥 / 𝑧 ] 𝑧 = 𝑥 → ( 𝑥 = 𝑦 → [ 𝑦 / 𝑧 ] 𝑧 = 𝑥 ) )
3	1 2	ax-mp	⊢ ( 𝑥 = 𝑦 → [ 𝑦 / 𝑧 ] 𝑧 = 𝑥 )