Theorem equsb1 2356

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 2340	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑥 = 𝑦) → [𝑦 / 𝑥]𝑥 = 𝑦)
2		id 22	. 2 ⊢ (𝑥 = 𝑦 → 𝑥 = 𝑦)
3	1, 2	mpg 1715	1 ⊢ [𝑦 / 𝑥]𝑥 = 𝑦

Syntax hints:   → wi 4  [wsb 1867

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034  ax-13 2234

This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-sb 1868

This theorem is referenced by:  sbequ8ALT  2395  sbie  2396  pm13.183  3313  exss  4858  bj-sbieOLD  32020  frege54cor1b  37208  sb5ALT  37752  sb5ALTVD  38171