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Theorem pm2.61iine 3077
 Description: Equality version of pm2.61ii 186. (Contributed by Scott Fenton, 13-Jun-2013.) (Proof shortened by Wolf Lammen, 25-Nov-2019.)
Hypotheses
Ref Expression
pm2.61iine.1 ((𝐴𝐶𝐵𝐷) → 𝜑)
pm2.61iine.2 (𝐴 = 𝐶𝜑)
pm2.61iine.3 (𝐵 = 𝐷𝜑)
Assertion
Ref Expression
pm2.61iine 𝜑

Proof of Theorem pm2.61iine
StepHypRef Expression
1 pm2.61iine.2 . 2 (𝐴 = 𝐶𝜑)
2 pm2.61iine.3 . . . 4 (𝐵 = 𝐷𝜑)
32adantl 485 . . 3 ((𝐴𝐶𝐵 = 𝐷) → 𝜑)
4 pm2.61iine.1 . . 3 ((𝐴𝐶𝐵𝐷) → 𝜑)
53, 4pm2.61dane 3074 . 2 (𝐴𝐶𝜑)
61, 5pm2.61ine 3070 1 𝜑
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 399   = wceq 1538   ≠ wne 2987 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 210  df-an 400  df-ne 2988 This theorem is referenced by:  fntpb  6950  elfiun  8881  dedekind  10795  mdsymi  30204
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