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Theorem bj-equsal1ti 34043
Description: Inference associated with bj-equsal1t 34042. (Contributed by BJ, 30-Sep-2018.)
Hypothesis
Ref Expression
bj-equsal1ti.1 𝑥𝜑
Assertion
Ref Expression
bj-equsal1ti (∀𝑥(𝑥 = 𝑦𝜑) ↔ 𝜑)

Proof of Theorem bj-equsal1ti
StepHypRef Expression
1 bj-equsal1ti.1 . 2 𝑥𝜑
2 bj-equsal1t 34042 . 2 (Ⅎ𝑥𝜑 → (∀𝑥(𝑥 = 𝑦𝜑) ↔ 𝜑))
31, 2ax-mp 5 1 (∀𝑥(𝑥 = 𝑦𝜑) ↔ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  wal 1526  wnf 1775
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-12 2167  ax-13 2381
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772  df-nf 1776
This theorem is referenced by:  bj-equsal1  34044  bj-equsal2  34045
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