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Theorem axc4i-o 34502
Description: Inference version of ax-c4 34488. (Contributed by NM, 3-Jan-1993.) (New usage is discouraged.)
Hypothesis
Ref Expression
axc4i-o.1 (∀𝑥𝜑𝜓)
Assertion
Ref Expression
axc4i-o (∀𝑥𝜑 → ∀𝑥𝜓)

Proof of Theorem axc4i-o
StepHypRef Expression
1 hba1-o 34501 . 2 (∀𝑥𝜑 → ∀𝑥𝑥𝜑)
2 axc4i-o.1 . 2 (∀𝑥𝜑𝜓)
31, 2alrimih 1791 1 (∀𝑥𝜑 → ∀𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1521
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-c5 34487  ax-c4 34488  ax-c7 34489
This theorem is referenced by:  hbae-o  34507  aev-o  34535  axc11n-16  34542  ax12indalem  34549  ax12inda2ALT  34550
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