Theorem sbequ5 2473

Description: Substitution does not change an identical variable specifier. Usage of this theorem is discouraged because it depends on ax-13 2380. (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 2441	. 2 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦
2	1	sbf 2282	1 ⊢ ([𝑤 / 𝑧]∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥 𝑥 = 𝑦)

Syntax hints:   ↔ wb 207  ∀wal 1545  [wsb 2073

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-10 2152  ax-11 2168  ax-12 2189  ax-13 2380

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-tru 1550  df-ex 1787  df-nf 1791  df-sb 2074

This theorem is referenced by: (None)