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Theorem pm2.61iine 2871
Description: Equality version of pm2.61ii 175. (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 480 . . 3 ((𝐴𝐶𝐵 = 𝐷) → 𝜑)
4 pm2.61iine.1 . . 3 ((𝐴𝐶𝐵𝐷) → 𝜑)
53, 4pm2.61dane 2868 . 2 (𝐴𝐶𝜑)
61, 5pm2.61ine 2864 1 𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382   = wceq 1474  wne 2779
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  df-ne 2781
This theorem is referenced by:  fntpb  6356  elfiun  8196  dedekind  10051  mdsymi  28460
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