Theorem axc4i-o 36557

Description: Inference version of ax-c4 36543. (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 36556	. 2 ⊢ (∀𝑥𝜑 → ∀𝑥∀𝑥𝜑)
2		axc4i-o.1	. 2 ⊢ (∀𝑥𝜑 → 𝜓)
3	1, 2	alrimih 1830	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 1802  ax-4 1816  ax-c5 36542  ax-c4 36543  ax-c7 36544

This theorem is referenced by:  hbae-o  36562  aev-o  36590  axc11n-16  36597  ax12indalem  36604  ax12inda2ALT  36605