Theorem equsb1 2526

Description: Substitution applied to an atomic wff. Usage of this theorem is discouraged because it depends on ax-13 2386. Use the weaker equsb1v 2108 if possible. (Contributed by NM, 10-May-1993.) (New usage is discouraged.)

Assertion

Ref	Expression
equsb1	⊢ [𝑦 / 𝑥]𝑥 = 𝑦

Proof of Theorem equsb1

Step	Hyp	Ref	Expression
1		sb2 2500	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑥 = 𝑦) → [𝑦 / 𝑥]𝑥 = 𝑦)
2		id 22	. 2 ⊢ (𝑥 = 𝑦 → 𝑥 = 𝑦)
3	1, 2	mpg 1794	1 ⊢ [𝑦 / 𝑥]𝑥 = 𝑦

Syntax hints:   → wi 4  [wsb 2065

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-10 2141  ax-12 2173  ax-13 2386

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-ex 1777  df-nf 1781  df-sb 2066

This theorem is referenced by:  sbequ8  2539  sbie  2540  pm13.183OLD  3659  frege54cor1b  40233  sb5ALT  40852  sb5ALTVD  41240