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Theorem uun132p1 41271
Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
uun132p1.1 (((𝜓𝜒) ∧ 𝜑) → 𝜃)
Assertion
Ref Expression
uun132p1 ((𝜑𝜓𝜒) → 𝜃)

Proof of Theorem uun132p1
StepHypRef Expression
1 3anass 1091 . . 3 ((𝜑𝜓𝜒) ↔ (𝜑 ∧ (𝜓𝜒)))
2 ancom 463 . . 3 ((𝜑 ∧ (𝜓𝜒)) ↔ ((𝜓𝜒) ∧ 𝜑))
31, 2bitri 277 . 2 ((𝜑𝜓𝜒) ↔ ((𝜓𝜒) ∧ 𝜑))
4 uun132p1.1 . 2 (((𝜓𝜒) ∧ 𝜑) → 𝜃)
53, 4sylbi 219 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398  w3a 1083
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 209  df-an 399  df-3an 1085
This theorem is referenced by: (None)
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