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Theorem im2anan9 587
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))
21adantr 274 . 2 ((𝜑𝜃) → (𝜓𝜒))
3 im2an9.2 . . 3 (𝜃 → (𝜏𝜂))
43adantl 275 . 2 ((𝜑𝜃) → (𝜏𝜂))
52, 4anim12d 333 1 ((𝜑𝜃) → ((𝜓𝜏) → (𝜒𝜂)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  im2anan9r  588  trin  4036  xpss12  4646  f1oun  5387  poxp  6129  brecop  6519  enq0sym  7252  genpdisj  7343  tgcl  12247  txlm  12462
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