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Theorem bj-nfs1 32411
Description: Shorter proof of nfs1 2364 (three essential steps instead of four). (Contributed by BJ, 2-May-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-nfs1.nf 𝑦𝜑
Assertion
Ref Expression
bj-nfs1 𝑥[𝑦 / 𝑥]𝜑

Proof of Theorem bj-nfs1
StepHypRef Expression
1 bj-nfs1t2 32410 . 2 (∀𝑥𝑦𝜑 → Ⅎ𝑥[𝑦 / 𝑥]𝜑)
2 bj-nfs1.nf . 2 𝑦𝜑
31, 2mpg 1721 1 𝑥[𝑦 / 𝑥]𝜑
Colors of variables: wff setvar class
Syntax hints:  wnf 1705  [wsb 1877
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-10 2016  ax-12 2044  ax-13 2245
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1702  df-nf 1707  df-sb 1878
This theorem is referenced by: (None)
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