Theorem nfsbOLD 2565

Description: Obsolete version of nfsb 2564 as of 25-Feb-2024. (Contributed by Mario Carneiro, 11-Aug-2016.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
nfsb.1	⊢ Ⅎ𝑧𝜑

Assertion

Ref	Expression
nfsbOLD	⊢ Ⅎ𝑧[𝑦 / 𝑥]𝜑

Distinct variable group:   𝑦,𝑧

Allowed substitution hints:   𝜑(𝑥,𝑦,𝑧)

Proof of Theorem nfsbOLD

Step	Hyp	Ref	Expression
1		axc16nf 2263	. 2 ⊢ (∀𝑧 𝑧 = 𝑦 → Ⅎ𝑧[𝑦 / 𝑥]𝜑)
2		nfsb.1	. . 3 ⊢ Ⅎ𝑧𝜑
3	2	nfsb4 2539	. 2 ⊢ (¬ ∀𝑧 𝑧 = 𝑦 → Ⅎ𝑧[𝑦 / 𝑥]𝜑)
4	1, 3	pm2.61i 184	1 ⊢ Ⅎ𝑧[𝑦 / 𝑥]𝜑

Syntax hints:  ∀wal 1534  Ⅎwnf 1783  [wsb 2068

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 1969  ax-7 2014  ax-10 2144  ax-11 2160  ax-12 2176  ax-13 2389

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1539  df-ex 1780  df-nf 1784  df-sb 2069

This theorem is referenced by: (None)