Theorem sbequ5 2465

Description: Substitution does not change an identical variable specifier. Usage of this theorem is discouraged because it depends on ax-13 2372. (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 2433	. 2 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦
2	1	sbf 2263	1 ⊢ ([𝑤 / 𝑧]∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥 𝑥 = 𝑦)

Syntax hints:   ↔ wb 205  ∀wal 1537  [wsb 2067

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-10 2137  ax-11 2154  ax-12 2171  ax-13 2372

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1542  df-ex 1783  df-nf 1787  df-sb 2068

This theorem is referenced by: (None)