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Theorem mpanlr1 717
Description: An inference based on modus ponens. (Contributed by NM, 30-Dec-2004.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)
Hypotheses
Ref Expression
mpanlr1.1 𝜓
mpanlr1.2 (((𝜑 ∧ (𝜓𝜒)) ∧ 𝜃) → 𝜏)
Assertion
Ref Expression
mpanlr1 (((𝜑𝜒) ∧ 𝜃) → 𝜏)

Proof of Theorem mpanlr1
StepHypRef Expression
1 mpanlr1.1 . . 3 𝜓
21jctl 561 . 2 (𝜒 → (𝜓𝜒))
3 mpanlr1.2 . 2 (((𝜑 ∧ (𝜓𝜒)) ∧ 𝜃) → 𝜏)
42, 3sylanl2 680 1 (((𝜑𝜒) ∧ 𝜃) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
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 195  df-an 384
This theorem is referenced by:  oecl  7481  omass  7524  oen0  7530  oeordi  7531  oewordri  7536  oeworde  7537
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