Theorem nfsbOLD 2544

Description: Obsolete version of nfsb 2543 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 2262	. 2 ⊢ (∀𝑧 𝑧 = 𝑦 → Ⅎ𝑧[𝑦 / 𝑥]𝜑)
2		nfsb.1	. . 3 ⊢ Ⅎ𝑧𝜑
3	2	nfsb4 2519	. 2 ⊢ (¬ ∀𝑧 𝑧 = 𝑦 → Ⅎ𝑧[𝑦 / 𝑥]𝜑)
4	1, 3	pm2.61i 185	1 ⊢ Ⅎ𝑧[𝑦 / 𝑥]𝜑

Syntax hints:  ∀wal 1537  Ⅎwnf 1786  [wsb 2070

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 1912  ax-6 1971  ax-7 2016  ax-10 2143  ax-11 2159  ax-12 2176  ax-13 2380

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 846  df-tru 1542  df-ex 1783  df-nf 1787  df-sb 2071

This theorem is referenced by: (None)