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Theorem jaao 708
Description: Inference conjoining and disjoining the antecedents of two implications. (Contributed by NM, 30-Sep-1999.)
Hypotheses
Ref Expression
jaao.1 (𝜑 → (𝜓𝜒))
jaao.2 (𝜃 → (𝜏𝜒))
Assertion
Ref Expression
jaao ((𝜑𝜃) → ((𝜓𝜏) → 𝜒))

Proof of Theorem jaao
StepHypRef Expression
1 jaao.1 . . 3 (𝜑 → (𝜓𝜒))
21adantr 274 . 2 ((𝜑𝜃) → (𝜓𝜒))
3 jaao.2 . . 3 (𝜃 → (𝜏𝜒))
43adantl 275 . 2 ((𝜑𝜃) → (𝜏𝜒))
52, 4jaod 706 1 ((𝜑𝜃) → ((𝜓𝜏) → 𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wo 697
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  pm3.48  774  prlem1  957  nford  1546  funun  5162  poxp  6122  nntri3or  6382
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