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Metamath Proof Explorer

Theorem el3v3

Description: If a proposition is implied by z e. _V (which is true, see vex ) and two other antecedents, then it is implied by these other antecedents. (Contributed by Peter Mazsa, 16-Oct-2020)

		Ref	Expression
	Hypothesis	el3v3.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝑧 ∈ V ) → 𝜃 )
	Assertion	el3v3	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		el3v3.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝑧 ∈ V ) → 𝜃 )
2		vex	⊢ 𝑧 ∈ V
3	2 1	mp3an3	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )