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Theorem bj-genl 32567
Description: Generalization rule on the left conjunct. See 19.27 2093. (Contributed by BJ, 7-Jul-2021.)
Hypothesis
Ref Expression
bj-genr.1 (𝜑𝜓)
Assertion
Ref Expression
bj-genl (∀𝑥𝜑𝜓)

Proof of Theorem bj-genl
StepHypRef Expression
1 bj-genr.1 . . . 4 (𝜑𝜓)
21simpli 474 . . 3 𝜑
32ax-gen 1720 . 2 𝑥𝜑
41simpri 478 . 2 𝜓
53, 4pm3.2i 471 1 (∀𝑥𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wa 384  wal 1479
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720
This theorem depends on definitions:  df-bi 197  df-an 386
This theorem is referenced by: (None)
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