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Theorem wl-mps 32917
Description: Replacing a nested consequent. A sort of modus ponens in antecedent position. (Contributed by Wolf Lammen, 20-Sep-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
wl-mps.1 (𝜑 → (𝜓𝜒))
wl-mps.2 ((𝜑𝜒) → 𝜃)
Assertion
Ref Expression
wl-mps ((𝜑𝜓) → 𝜃)

Proof of Theorem wl-mps
StepHypRef Expression
1 wl-mps.1 . . 3 (𝜑 → (𝜓𝜒))
21a2i 14 . 2 ((𝜑𝜓) → (𝜑𝜒))
3 wl-mps.2 . 2 ((𝜑𝜒) → 𝜃)
42, 3syl 17 1 ((𝜑𝜓) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  wl-syls1  32918
  Copyright terms: Public domain W3C validator