Theorem sbequ5 2464

Description: Substitution does not change an identical variable specifier. Usage of this theorem is discouraged because it depends on ax-13 2371. (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 2432	. 2 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦
2	1	sbf 2269	1 ⊢ ([𝑤 / 𝑧]∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥 𝑥 = 𝑦)

Syntax hints:   ↔ wb 209  ∀wal 1541  [wsb 2072

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2018  ax-10 2143  ax-11 2160  ax-12 2177  ax-13 2371

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-tru 1546  df-ex 1788  df-nf 1792  df-sb 2073

This theorem is referenced by: (None)