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Theorem wl-equsalcom 33656
Description: This simple equivalence eases substitution of one expression for the other. (Contributed by Wolf Lammen, 1-Sep-2018.)
Assertion
Ref Expression
wl-equsalcom (∀𝑥(𝑥 = 𝑦𝜑) ↔ ∀𝑥(𝑦 = 𝑥𝜑))

Proof of Theorem wl-equsalcom
StepHypRef Expression
1 equcom 2102 . . 3 (𝑥 = 𝑦𝑦 = 𝑥)
21imbi1i 338 . 2 ((𝑥 = 𝑦𝜑) ↔ (𝑦 = 𝑥𝜑))
32albii 1894 1 (∀𝑥(𝑥 = 𝑦𝜑) ↔ ∀𝑥(𝑦 = 𝑥𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1628
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1852
This theorem is referenced by:  wl-equsal1i  33657
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