Theorem imasor-P4.32a 487

Description: '→' in Terms of '∨'.

Assertion

Ref	Expression
imasor-P4.32a	⊢ ((𝜑 → 𝜓) ↔ (¬ 𝜑 ∨ 𝜓))

Proof of Theorem imasor-P4.32a

Step	Hyp	Ref	Expression
1		imasor-P4.32-L1 485	. 2 ⊢ ((𝜑 → 𝜓) → (¬ 𝜑 ∨ 𝜓))
2		imasor-P4.32-L2 486	. 2 ⊢ ((¬ 𝜑 ∨ 𝜓) → (𝜑 → 𝜓))
3	1, 2	rcp-NDBII0 239	1 ⊢ ((𝜑 → 𝜓) ↔ (¬ 𝜑 ∨ 𝜓))

Syntax hints:  ¬ wff-neg 9   → wff-imp 10   ↔ wff-bi 104   ∨ wff-or 144

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-or-D2.3 145  df-true-D2.4 155

This theorem is referenced by:  imasand-P4.33a  489  biasandor-P4.34a  491  qimeqallhalf-P5  609  qimeqex-P5-L1  610  dfnfreealt-P6  683  psubim-P6-L2  790  dfnfree-P7  968