Theorem 19.21bi 1558

Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
19.21bi.1	⊢ (𝜑 → ∀𝑥𝜓)

Assertion

Ref	Expression
19.21bi	⊢ (𝜑 → 𝜓)

Proof of Theorem 19.21bi

Step	Hyp	Ref	Expression
1		19.21bi.1	. 2 ⊢ (𝜑 → ∀𝑥𝜓)
2		ax-4 1510	. 2 ⊢ (∀𝑥𝜓 → 𝜓)
3	1, 2	syl 14	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∀wal 1351

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1510

This theorem is referenced by:  19.21bbi  1559  ax11e  1796  eqeq1  2184  eleq2  2241  r19.21bi  2565  elrab3t  2893  ssel  3150  exmidsssn  4203  copsex2t  4246  pocl  4304  ordsucim  4500  peano2  4595  funmo  5232  funun  5261  fununi  5285  imain  5299  tfrlem3-2d  6313  tfr1onlemaccex  6349  tfri1dALT  6352  tfrcllemaccex  6362  findcard  6888  findcard2  6889  findcard2s  6890  exmidpw  6908  exmidpweq  6909