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Theorem bj-genr 34025
Description: Generalization rule on the right conjunct. See 19.28 2232. (Contributed by BJ, 7-Jul-2021.)
Hypothesis
Ref Expression
bj-genr.1 (𝜑𝜓)
Assertion
Ref Expression
bj-genr (𝜑 ∧ ∀𝑥𝜓)

Proof of Theorem bj-genr
StepHypRef Expression
1 bj-genr.1 . . 3 (𝜑𝜓)
21simpli 487 . 2 𝜑
31simpri 489 . . 3 𝜓
43ax-gen 1797 . 2 𝑥𝜓
52, 4pm3.2i 474 1 (𝜑 ∧ ∀𝑥𝜓)
Colors of variables: wff setvar class
Syntax hints:  wa 399  wal 1536
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797
This theorem depends on definitions:  df-bi 210  df-an 400
This theorem is referenced by: (None)
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