Theorem sbequ5 2470

Description: Substitution does not change an identical variable specifier. Usage of this theorem is discouraged because it depends on ax-13 2377. (Contributed by NM, 15-May-1993.) (New usage is discouraged.)

Assertion

Ref	Expression
sbequ5	⊢ ([𝑤 / 𝑧]∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥 𝑥 = 𝑦)

Proof of Theorem sbequ5

Step	Hyp	Ref	Expression
1		nfae 2438	. 2 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦
2	1	sbf 2272	1 ⊢ ([𝑤 / 𝑧]∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥 𝑥 = 𝑦)

Syntax hints:   ↔ wb 206  ∀wal 1538  [wsb 2065

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-10 2142  ax-11 2158  ax-12 2178  ax-13 2377

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-nf 1784  df-sb 2066

This theorem is referenced by: (None)