Theorem axc4i-o 40158

Description: Inference version of ax-c4 40144. (Contributed by NM, 3-Jan-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
axc4i-o.1	⊢ (∀𝑥𝜑 → 𝜓)

Assertion

Ref	Expression
axc4i-o	⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

Proof of Theorem axc4i-o

Step	Hyp	Ref	Expression
1		hba1-o 40157	. 2 ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑)
2		axc4i-o.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimih 1857	1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓)

This proof depends on syntax axioms:   → wi 4  ∀wal 1568

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-c5 40143  ax-c4 40144  ax-c7 40145

This theorem is used by:  hbae-o  40163  aev-o  40191  axc11n-16  40198  ax12indalem  40205  ax12inda2ALT  40206