Theorem sbequ6 2457

Description: Substitution does not change a distinctor. Usage of this theorem is discouraged because it depends on ax-13 2363. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.)

Assertion

Ref	Expression
sbequ6	⊢ ([𝑤 / 𝑧] ¬ ∀𝑥 𝑥 = 𝑦 ↔ ¬ ∀𝑥 𝑥 = 𝑦)

Proof of Theorem sbequ6

Step	Hyp	Ref	Expression
1		nfnae 2425	. 2 ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦
2	1	sbf 2254	1 ⊢ ([𝑤 / 𝑧] ¬ ∀𝑥 𝑥 = 𝑦 ↔ ¬ ∀𝑥 𝑥 = 𝑦)

Syntax hints:  ¬ wn 3   ↔ wb 205  ∀wal 1531  [wsb 2059

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-10 2129  ax-11 2146  ax-12 2163  ax-13 2363

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-nf 1778  df-sb 2060

This theorem is referenced by: (None)