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Theorem bj-exlimmp 9178
Description: Lemma for bj-vtoclgf 9184. (Contributed by BJ, 21-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-exlimmp.nf xψ
bj-exlimmp.min (χφ)
Assertion
Ref Expression
bj-exlimmp (x(χ → (φψ)) → (xχψ))

Proof of Theorem bj-exlimmp
StepHypRef Expression
1 nfa1 1431 . 2 xx(χ → (φψ))
2 bj-exlimmp.nf . 2 xψ
3 bj-exlimmp.min . . . . 5 (χφ)
4 idd 21 . . . . 5 (χ → (ψψ))
53, 4embantd 50 . . . 4 (χ → ((φψ) → ψ))
65a2i 11 . . 3 ((χ → (φψ)) → (χψ))
76sps 1427 . 2 (x(χ → (φψ)) → (χψ))
81, 2, 7exlimd 1485 1 (x(χ → (φψ)) → (xχψ))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240  wnf 1346  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie2 1380  ax-4 1397  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  bj-vtoclgft  9183
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