Theorem equsb1 2499

Description: Substitution applied to an atomic wff. (Contributed by NM, 10-May-1993.)

Assertion

Ref	Expression
equsb1	⊢ [𝑦 / 𝑥]𝑥 = 𝑦

Proof of Theorem equsb1

Step	Hyp	Ref	Expression
1		sb2 2482	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑥 = 𝑦) → [𝑦 / 𝑥]𝑥 = 𝑦)
2		id 22	. 2 ⊢ (𝑥 = 𝑦 → 𝑥 = 𝑦)
3	1, 2	mpg 1896	1 ⊢ [𝑦 / 𝑥]𝑥 = 𝑦

Syntax hints:   → wi 4  [wsb 2067

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-12 2220  ax-13 2389

This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1879  df-sb 2068

This theorem is referenced by:  sbequ8ALT  2538  sbie  2539  pm13.183  3563  exss  5154  frege54cor1b  39023  sb5ALT  39564  sb5ALTVD  39962