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Theorem bj-hbsb3 36157
Description: Shorter proof of hbsb3 2478. (Contributed by BJ, 2-May-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-hbsb3.1 (𝜑 → ∀𝑦𝜑)
Assertion
Ref Expression
bj-hbsb3 ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑)

Proof of Theorem bj-hbsb3
StepHypRef Expression
1 bj-hbsb3t 36156 . 2 (∀𝑥(𝜑 → ∀𝑦𝜑) → ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑))
2 bj-hbsb3.1 . 2 (𝜑 → ∀𝑦𝜑)
31, 2mpg 1791 1 ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1531  [wsb 2059
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-10 2129  ax-12 2163  ax-13 2363
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-ex 1774  df-nf 1778  df-sb 2060
This theorem is referenced by: (None)
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