Theorem a5i 1789

Description: Inference version of ax5o 1749. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
a5i.1	⊢ (∀xφ → ψ)

Assertion

Ref	Expression
a5i	⊢ (∀xφ → ∀xψ)

Proof of Theorem a5i

Step	Hyp	Ref	Expression
1		nfa1 1788	. 2 ⊢ Ⅎx∀xφ
2		a5i.1	. 2 ⊢ (∀xφ → ψ)
3	1, 2	alrimi 1765	1 ⊢ (∀xφ → ∀xψ)

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by:  hbae  1953  hbsb2a  2041  hbsb2e  2042  hbsb2  2057  reu6  3026