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Theorem bibi1d 222
Description: Deduction adding a biconditional to the right in an equivalence. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
imbid.1 (φ → (ψχ))
Assertion
Ref Expression
bibi1d (φ → ((ψθ) ↔ (χθ)))

Proof of Theorem bibi1d
StepHypRef Expression
1 imbid.1 . . 3 (φ → (ψχ))
21bibi2d 221 . 2 (φ → ((θψ) ↔ (θχ)))
3 bicom 128 . 2 ((ψθ) ↔ (θψ))
4 bicom 128 . 2 ((χθ) ↔ (θχ))
52, 3, 43bitr4g 212 1 (φ → ((ψθ) ↔ (χθ)))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  bibi12d  224  bibi1  229  biassdc  1267  eubidh  1884  eubid  1885  axext3  2001  bm1.1  2003  eqeq1  2024  pm13.183  2654  elabgt  2657  elrab3t  2670  mob  2696  sbctt  2797  sbcabel  2812  isoeq2  5363  caovcang  5581  bdsepnft  7252  bdsepnfALT  7254  strcollnft  7341  strcollnfALT  7343
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