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Theorem simplim 163
Description: Simplification. Similar to Theorem *3.26 (Simp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Wolf Lammen, 21-Jul-2012.)
Assertion
Ref Expression
simplim (¬ (𝜑𝜓) → 𝜑)

Proof of Theorem simplim
StepHypRef Expression
1 pm2.21 120 . 2 𝜑 → (𝜑𝜓))
21con1i 144 1 (¬ (𝜑𝜓) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  pm2.5  164  pm2.521  166  impt  169  peirce  193  dfbi1  203  biimp  205  imbi12  336  pm4.79  606  mptbi12f  33646  ac6s6  33651  rp-fakeimass  37377
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