Theorem nfanOLDOLD 2225

Description: Obsolete proof of nfan 1816 as of 6-Oct-2021. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 13-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfanOLDOLD.1	⊢ Ⅎ𝑥𝜑
nfanOLDOLD.2	⊢ Ⅎ𝑥𝜓

Assertion

Ref	Expression
nfanOLDOLD	⊢ Ⅎ𝑥(𝜑 ∧ 𝜓)

Proof of Theorem nfanOLDOLD

Step	Hyp	Ref	Expression
1		nfanOLDOLD.1	. 2 ⊢ Ⅎ𝑥𝜑
2		nfanOLDOLD.2	. . 3 ⊢ Ⅎ𝑥𝜓
3	2	a1i 11	. 2 ⊢ (𝜑 → Ⅎ𝑥𝜓)
4	1, 3	nfan1OLD 2224	1 ⊢ Ⅎ𝑥(𝜑 ∧ 𝜓)

Syntax hints:   ∧ wa 383  ℲwnfOLD 1700

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-nfOLD 1712

This theorem is referenced by:  nfnanOLD  2226  nf3anOLD  2227  hbanOLD  2228