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Theorem wl-motae 34626
Description: Change bound variable. Uses only Tarski's FOL axiom schemes. Part of Lemma 7 of [KalishMontague] p. 86. (Contributed by Wolf Lammen, 5-Mar-2023.)
Assertion
Ref Expression
wl-motae (∃*𝑢⊤ → ∀𝑥 𝑦 = 𝑧)

Proof of Theorem wl-motae
Dummy variable 𝑣 is distinct from all other variables.
StepHypRef Expression
1 wl-cbvmotv 34624 . 2 (∃*𝑢⊤ → ∃*𝑣⊤)
2 wl-moteq 34625 . . 3 (∃*𝑣⊤ → 𝑦 = 𝑧)
32alrimiv 1921 . 2 (∃*𝑣⊤ → ∀𝑥 𝑦 = 𝑧)
41, 3syl 17 1 (∃*𝑢⊤ → ∀𝑥 𝑦 = 𝑧)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1528  wtru 1531  ∃*wmo 2617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008
This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1533  df-ex 1774  df-mo 2619
This theorem is referenced by:  wl-moae  34627
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