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Theorem bj-equsal1ti 31998
 Description: Inference associated with bj-equsal1t 31997. (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 31997 . 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 195  ∀wal 1473  Ⅎwnf 1699 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034  ax-13 2234 This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-nf 1701 This theorem is referenced by:  bj-equsal1  31999  bj-equsal2  32000
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