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Theorem dflb 93
Description: Nicer definition of biconditional. Uses and .
Assertion
Ref Expression
dflb ((𝜑𝜓) ⧟ ((𝜑𝜓) & (𝜓𝜑)))

Proof of Theorem dflb
StepHypRef Expression
1 dflb1s 91 . . 3 ((𝜑𝜓) ⊸ ((𝜑𝜓) & (𝜓𝜑)))
2 dflb2s 92 . . 3 (((𝜑𝜓) & (𝜓𝜑)) ⊸ (𝜑𝜓))
31, 2iaci 36 . 2 (((𝜑𝜓) ⊸ ((𝜑𝜓) & (𝜓𝜑))) & (((𝜑𝜓) & (𝜓𝜑)) ⊸ (𝜑𝜓)))
4 dflb2s 92 . 2 ((((𝜑𝜓) ⊸ ((𝜑𝜓) & (𝜓𝜑))) & (((𝜑𝜓) & (𝜓𝜑)) ⊸ (𝜑𝜓))) ⊸ ((𝜑𝜓) ⧟ ((𝜑𝜓) & (𝜓𝜑))))
53, 4lmp 76 1 ((𝜑𝜓) ⧟ ((𝜑𝜓) & (𝜓𝜑)))
Colors of variables: wff var nilad
Syntax hints:   & wac 30  wlb 55  wli 61
This theorem was proved from axioms:  ax-ibot 4  ax-ebot 5  ax-cut 6  ax-init 7  ax-mdco 8  ax-mdas 9  ax-iac 32  ax-eac1 33  ax-eac2 34
This theorem depends on definitions:  df-lb 56  df-li 62
This theorem is referenced by:  ilb  96  ilbd  97  lbsymd  102  abs1  178
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