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Theorem exlimiieq2 33099
Description: Inferring a theorem when it is implied by an equality which may be true. (Contributed by BJ, 15-Sep-2018.) (Revised by BJ, 30-Sep-2018.)
Hypotheses
Ref Expression
exlimiieq2.1 𝑦𝜑
exlimiieq2.2 (𝑥 = 𝑦𝜑)
Assertion
Ref Expression
exlimiieq2 𝜑

Proof of Theorem exlimiieq2
StepHypRef Expression
1 exlimiieq2.1 . 2 𝑦𝜑
2 exlimiieq2.2 . 2 (𝑥 = 𝑦𝜑)
3 ax6er 33097 . 2 𝑦 𝑥 = 𝑦
41, 2, 3exlimii 33095 1 𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4  wnf 1845
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1859  ax-4 1874  ax-5 1976  ax-6 2042  ax-7 2078  ax-12 2184  ax-13 2379
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1842  df-nf 1847
This theorem is referenced by: (None)
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