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Theorem im2anan9 619
Description: Deduction joining nested implications to form implication of conjunctions. (Contributed by NM, 29-Feb-1996.)
Hypotheses
Ref Expression
im2an9.1 (𝜑 → (𝜓𝜒))
im2an9.2 (𝜃 → (𝜏𝜂))
Assertion
Ref Expression
im2anan9 ((𝜑𝜃) → ((𝜓𝜏) → (𝜒𝜂)))

Proof of Theorem im2anan9
StepHypRef Expression
1 im2an9.1 . . 3 (𝜑 → (𝜓𝜒))
21adantrd 491 . 2 (𝜑 → ((𝜓𝜏) → 𝜒))
3 im2an9.2 . . 3 (𝜃 → (𝜏𝜂))
43adantld 490 . 2 (𝜃 → ((𝜓𝜏) → 𝜂))
52, 4anim12ii 617 1 ((𝜑𝜃) → ((𝜓𝜏) → (𝜒𝜂)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 206  df-an 396
This theorem is referenced by:  im2anan9r  620  anim12  806  trin  5277  somo  5625  xpss12  5691  f1oun  6852  poxp  8118  soxp  8119  brecop  8808  ingru  10814  genpss  11003  genpnnp  11004  tgcl  22693  txlm  23373  upgrpredgv  28667  3wlkdlem4  29683  frgrwopreglem5  29842  frgrwopreglem5ALT  29843  icorempo  36536  ax12eq  38115  ax12el  38116  odd2prm2  46685
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