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Metamath Proof Explorer

Theorem pm4.42

Description: Theorem *4.42 of WhiteheadRussell p. 119. See also ifpid . (Contributed by Roy F. Longton, 21-Jun-2005)

		Ref	Expression
	Assertion	pm4.42	⊢ ( 𝜑 ↔ ( ( 𝜑 ∧ 𝜓 ) ∨ ( 𝜑 ∧ ¬ 𝜓 ) ) )

Step	Hyp	Ref	Expression
1		dedlema	⊢ ( 𝜓 → ( 𝜑 ↔ ( ( 𝜑 ∧ 𝜓 ) ∨ ( 𝜑 ∧ ¬ 𝜓 ) ) ) )
2		dedlemb	⊢ ( ¬ 𝜓 → ( 𝜑 ↔ ( ( 𝜑 ∧ 𝜓 ) ∨ ( 𝜑 ∧ ¬ 𝜓 ) ) ) )
3	1 2	pm2.61i	⊢ ( 𝜑 ↔ ( ( 𝜑 ∧ 𝜓 ) ∨ ( 𝜑 ∧ ¬ 𝜓 ) ) )