Theorem alrimd 2207

Description: Deduction form of Theorem 19.21 of [Margaris] p. 90, see 19.21 2199. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

Ref	Expression
alrimd.1	⊢ Ⅎ𝑥𝜑
alrimd.2	⊢ Ⅎ𝑥𝜓
alrimd.3	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
alrimd	⊢ (𝜑 → (𝜓 → ∀𝑥𝜒))

Proof of Theorem alrimd

Step	Hyp	Ref	Expression
1		alrimd.1	. 2 ⊢ Ⅎ𝑥𝜑
2		alrimd.2	. . 3 ⊢ Ⅎ𝑥𝜓
3	2	a1i 11	. 2 ⊢ (𝜑 → Ⅎ𝑥𝜓)
4		alrimd.3	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
5	1, 3, 4	alrimdd 2206	1 ⊢ (𝜑 → (𝜓 → ∀𝑥𝜒))

Syntax hints:   → wi 4  ∀wal 1538  Ⅎwnf 1784

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-12 2170

This theorem depends on definitions:  df-bi 206  df-ex 1781  df-nf 1785

This theorem is referenced by:  moexexlem  2621  ralrimd  3260  pssnn  9174  pssnnOLD  9271  fiint  9330  wl-mo3t  36905  pm14.24  43654