Theorem a5i-o 2150

Description: Inference version of ax-5o 2136. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.)

Hypothesis

Ref	Expression
a5i-o.1	⊢ (∀xφ → ψ)

Assertion

Ref	Expression
a5i-o	⊢ (∀xφ → ∀xψ)

Proof of Theorem a5i-o

Step	Hyp	Ref	Expression
1		hba1-o 2149	. 2 ⊢ (∀xφ → ∀x∀xφ)
2		a5i-o.1	. 2 ⊢ (∀xφ → ψ)
3	1, 2	alrimih 1565	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-4 2135  ax-5o 2136  ax-6o 2137

This theorem is referenced by:  hbae-o  2153  aev-o  2182  ax10-16  2190  ax11indalem  2197  ax11inda2ALT  2198